Stochastic Learning Automata (LA) are probabilistic finite state machines which have been used to model how biological systems can learn. The structure of such a machine can be fixed, or it can be changing with time A LA can also be implemented by using action probability updating rules which may or may not depend on estimates from the Environment being investigated. During the initial years of research in the field of LA, these updating rules worked with the continuous probability space. In this paper, we will describe how LA can also be designed by discretizing the probability space. The paper¹ will describe the design and analysis of both continuous and discretized LA, and will highlight the subtle differences between the corresponding learning machines, their convergence properties, and their learning capabilities.

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Both single and repeated stimuli produce waves of activity in the visual cortex of freshwater turtles. Large scale, biophysically realistic models of the retina and the visual cortex capture the basic features of the waves produced by a single stimuli. The waves produced are subsequently represented using principal components obtained over a sequence of time windows. The locations and velocities of the stimuli are detected from these representations using maximum likelihood estimates.

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This paper is concerned with the identification of a discrete-time Wiener model, composed of a linear time-invariant (LTI) system and a static nonlinearity. Introducing a set of basis functions for the nonlinearity, we employ an output error criterion for the Wiener model identification. We apply the separable least-squares method to develop a two-stage method that identifies the LTI system using the data driven local coordinate (DDLC) and estimates coefficients of the nonlinearity by a simple substitution. Two examples are included.

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This paper proposes a method for signal recovery from noisy observation in system identification. From an ICA (Independent Component Analysis) point of view, this method estimates the noise model by resorting the problem to what is called semi-blind deconvolution, and then cancels the noise effect, thereby enabling us to identify the system more accurately. An adaptive (on-line) semi-blind method is described with focus upon the cost function. Numerical example for a spring-mass-damper system illustrates the result.

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This paper studies the asymptotic behavior of the solution to the Riccati difference equation for stochastic realization [1] as the time progresses, by using the results of[2]. It is alternatively proved that the solution to the Riccati difference equation converges to the stabilizing solution to the steady state Riccati equation. Numerical simulation results are also included.

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The Real-Time Kinematic (RTK) Global Positioning System (GPS) with Kalman filtering estimates the position and velocity of automobiles and so on by using dynamical models. If the dynamical model is not appropriate for automobile movements, the accuracy of the predicted position and velocity decreases. In this case, when the methods statistically test whether cycle slips (i.e., sudden jumps in the carrier phase observation by an integer number of cycles) occur, using the difference between observation and prediction, the inadequate dynamical models cause the mis-detections of cycle slips. To prevent these mis-detections we proposed a dynamical model in which the jerk is assumed to be a first-order Markov process (jerk model), but we did not demonstrate that this jerk model fit the automobile movements. It was therefore necessary to show that the time series data in different time intervals fit the same jerk model i.e., that the jerk model is a stationary autoregressive model. This paper describes the method that decides whether the autoregressive model is stationary. The stationarity of the jerk model is analyzed by using observation data collected with a car. Moreover, the cycle slip detection performance of the jerk model is compared with that of another model, and it is shown that the performance of the jerk model is improved.

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In the manufacturing business, the delivery guarantee of quantities is a prerequisite for improving the credit of corporation and securing profit. However, the delivery quantity, the production quantity, and the inventory is changed according to various unexpected reasons. Then the prediction of production and inventory which can cope with such irregular fluctuations is required. This paper deals with an adjusting production method using the Dynamic Bayesian Network (DBN) for all factors which influence the production quantity, the delivery quantity, and the inventory quantity for an automobile parts production process. This study also provides an adjusting production schedule algorithm that adjusts sequentially the production schedule for appropriate guarantee of the deadline. Furthermore, an adjusting rule of the production quantities to maintain the delivery guarantee is provided.

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In recent years, the traffic congestion has become serious problem with the number of automobiles increased significantly. The traffic signal control is one of the effective ways to solve the problem.The traffic forecasting has been known as an important part of the traffic signal control, and the random walk method, Neuron Network, and Bayesian Network are known as these methods, however the methods do not use the information for neighboring roads.In this paper, a Dynamic Bayesian networks (DBN) model to predict the probabilistic distribution of the standing vehicles is constructed based on the information of the neighboring roads, and the traffic signal control method is proposed.

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In this paper we study the stochastic optimal tracking problems with preview for a class of linear discrete-time Markovian jump systems. The systems are described by the discrete-time switching systems with Markovian mode transitions. The necessary and sufficient conditions for the solvability of our optimal tracking problems are given by coupled Riccati difference equations with terminal conditions. Correspondingly feedforward compensators introducing future information are given by coupled difference equations with terminal conditions. We consider three different tracking problems depending on the property of the reference signals. Finally we give numerical examples.

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In this paper, a method of risk-sensitive stabilization of a parallel structured single-link flexible arm using Kalman filter based LEQG control is presented. This arm is assumed to receive random disturbance which is generated by moving base such as vehicle bodies, mobile robots and so on. The random disturbance due to the moving base depends on its unknown acceleration which is assumed to be modeled by the white Gaussian noise. The structure of the arm is approximated by a single-link flexible arm consisting of an Euler-Bernoulli beam with the same boundary conditions of the parallel-structured one. The LEQG controller and the Kalman filter are constructed for the finite-dimensional model corresponding to the simplified structure model.

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In this paper, we study nonparametric density estimation from quantized samples. Since quantization decreases the amount of information, interpolation (or estimation) of the missing information is needed. To achieve this, we introduce sampled-data H∞ control theory to optimize the worst case error between the original probability density function and the estimation. The optimization is formulated by linear matrix inequalities and equalities. A numerical example is illustrated to show the effectiveness of our method.

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In this paper, we are concerned with an optimal selection of the gain matrix of the noisy observation for stationary LQG stochastic control systems. By introducing an information theoretic criterion based on a generalized Water Filling Theorem, we obtain a set of the gains which maximize the mutual information between the system state and the observations. Then, equations are obtained to find the optimal gain matrix from this set of gains which produces the best performance of the optimal LQG regulator.

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A method of on-line residual life estimation is proposed for condition based maintenance of industrial equipment. With on-line monitoring of the condition of the equipment, the residual life is estimated by using on-line prediction of the equipment deterioration. The deterioration prediction is based on the on-line identification of the mathematical model of deterioration. To improve the accuracy of the deterioration prediction, outlier elimination technique is adopted in the on-line identification algorithm. Simulation study was carried out in order to assure the effectiveness of the proposed on-line residual life estimation method. The proposed method was also applied to actual data of rotating equipment in a thermal power plant and an appropriate residual life estimation result was obtained.

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A novel finite impulse response (FIR) adaptive filter algorithm was proposed for system identification based on independent component analysis (ICA). It shows an excellent robustness for non-Gaussian disturbance. In this paper, we discuss various properties of this ICA-based adaptive filter algorithm, including the role of the scaling paramter, the local stability condition and a performance analysis by calculating the estimation error covariance matrix using the ordinary differential equation (ODE) approach.

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In this paper we develop identification methods for IMU (Inertial Measurement Unit) sensor error models in the GPS/INS hybrid systems. GPS provides high-accuracy position, velocity. The main factor limiting the use of GPS is the requirement for line-of-sight between the receiver antenna and the satellites. On the other hand, an Inertial Navigation System (INS) provides position, velocity and attitude autonomously at a rate of several tens of Hz. However, its errors are accumulated owing to drift of IMU. In order to overcome the inherent drawbacks of each system, integrated GPS/INS systems have been developed. In this paper, for more accurate positioning, we develop the identification methods for IMU sensor error models in the hybrid navigation system.In the hybrid navigation for keeping accurate positioning, GPS/IMU coupled methods and filtering techniques have being investigated for past two decades. IMU sensor errors models (bias, scale factor, noise) are assumed as stochastic models such as Gauss Markov (GM) model. For most navigation-grade IMU such as ring laser gyro (RLG), 1st order Gauss-Markov models are usually used for the hybrid navigation. This is also true for low-cost IMU sensors such as fiber optical gyro (FOG) and micro electro mechanical systems (MEMS) although sometimes a random walk process is utilized instead. In this paper, we discuss IMU stochastic error modeling applying autoregressive (AR) models of orders higher than one [2]. Namely, the IMU sensor errors are modeled as the high-order vector autoregressive (VAR) models. The best order of AR models is determined by Akaike's information criterion [1].First, we discuss nonlinear filtering construct and In-Motion alignment methods to estimate the initial attitude and heading of INS. Next, we examine sensor error model and sensor error state equation. Based on the above method we show the experimental results under considering the static situation. The sensor error models applying VAR models execute the decreasing of error factor of AR coefficient by considering of axis correlation.

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The pseudomeasurement approach which was developed by the authors is applied to identify the exogenous input whose form is quite unknown.

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A history based particle filter is introduced for state estimation of problems of stochastic hybrid systems. A multiple hypothesis approach to particle filters is proposed to estimate system states and modes simultaneously. The hypotheses are composed by possible mode sequences, then particle filters are applied to each hypothesis to test which hypothesis is the most acceptable. A performance of the proposed approach compared with a standard particle filter and the interactive multiple model based particle filter is discussed based on the numerical simulations.

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In this paper, the method of consistent estimation of the EIV models based on the quantized input-output measurements is studied. A new bias-compensation based method, named the bias-compensated instrumental variable type (BCIV-type) method, has been proposed for the quantized EIV models identification. The proposed BCIV-type method is based on compensation of asymptotic bias on the instrumental variable type (IV-type) estimates by making use of noises variances and quantization errors variances estimates. It is demonstrated that the proposed method can give consistent parameter estimate via simulation results.

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In an estimation problem of the state or parameters in nonlinear systems, it is required to linearlize the original nonlinear system model. More recently, a statistical linear regression(SLR) method has been proposed for the linearlization. This technique is superior to Taylor series expansion-based ones.In this report, a method of treatment for the linearlization error arisen in the SLR linearization is proposed. Concretely, it is treated as a part of the state of the systems.A numerical experiment indicates acceptable performance of proposed method.

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In this paper, we present an identification algorithm for discrete-time multiple-input multiple-output (MIMO) state-space models with colored noise observation. It is assumed that the system is the model with the colored noise observation. The parametric discrete-time canonical-formed MIMO state-space model is identified based on Maximum-Likelihood (ML) and Akaike's Information Criterion (AIC). To obtain the maximum-likelihood estimates of the model parameter, we apply Expectation-Maximization (EM) algorithms which are iterative methods such that the choice of the initial estimates is most important. The initial estimates parameter in canonical-formed state-space models are obtained by N4SID [1] methods.

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Large-scale linear programming problems whose coefficients are random variables will be considered in this paper. Stability of the optimum solutions of these problems as the number of variables increases was shown in terms of the laws of large numbers by Kuhn and Quandt (on the weak law) and by Prékopa (on the strong law). The same conclusions were proved for a broader class of problems under weaker assumptions in the previous paper. Here, we prove the laws of large numbers under even weaker assumptions for independent and identically distributed (i.i.d.) random variables by applying an estimate by Brillinger and Petrov. We give a simple example which shows that the assumption r ≥ 2 associated with the moment condition given in Proposition 3.1 cannot be replaced by the weaker assumption 0 ＜ r ＜ 2.

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Stability of the particle swarm optimization algorithm is analyzed without any simplifying assumptions made in the previous works. To evaluate the convergence speed of the algorithm, the decay rate is introduced, and a method for finding the largest lower bound of the decay rate is presented. The proposed method is based on linear matrix inequality techniques, and therefore is carried out efficiently by using convex optimization tools. Numerical examples are given to show that the analysis method is reasonable and effective to select the parameters in the algorithm.

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A randomized algorithm is proposed for solving a robust optimization which is to minimize a convex objective function subject to a parameter dependent convex constraint. The probabilistic analytic center cutting plane method is employed for solving a series of robust feasibility problems defined by an optimality cut which corresponds to a provisional optimal value, where the parameter is randomly sampled in each iteration and the cut is sequentially updated for optimization. The algorithm always stops in a finite number of iterations, and finds a suboptimal solution and a suboptimal value. The suboptimal solution satisfies the constraint with a given probability and with a given probabilistic confidence, while the suboptimal value ensures that the feasibility set whose objective function is less than this value is too small to contain a ball with a given radius. The upper bounds of the numbers of random samples and updates of the algorithm are of polynomial order of the problem size.

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Differential evolution (DE) is one of the evolutionary algorithms. DE has excellent ability for searching global optimum over continuous spaces. This paper introduces a modified DE algorithm called the differential evolution with adaptive neighborhood for locating all the global optima of multimodal functions. The proposed method form a neighborhood using euclidean distance between individuals, re-form the neighborhood at prescribed generations. The proposed method can independently locate global optima in each neighborhood by dividing population into multiple neighborhood. In real world optimization problems, multiple global optima and local optima are required frequently, along with an unique global optimum. This proposed method is one of improvements for these real world optimization problems. The performance of the proposed method is evaluated with several multimodal function optimization problems. The experimental results show good performance better than original DE algorithm.

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A revised Group Method of Data Handling (GMDH)-type neural network algorithm for medical image recognition is proposed and is applied to 3-dimensional medical image analysis of the heart. In this algorithm, the optimum neural network architecture fitting the complexity of the medical images is automatically organized using the heuristic self-organization method and the structural parameters such as the number of feedback loops, the number of neurons in the hidden layer and useful input variables are automatically selected so as to minimize the prediction error criterion defined as Prediction Sum of Squares (PSS).

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In this paper, we present an image restoration technique for noiseless circular motion blurred images. To simulate the circular motion blurred images, we create circular paths by applying the Bresenham line algorithm. The algorithm can simplify the spatially variant image restoration problem into the spatially invariant one. Since the degradation process along the circular blurring paths is spatially invariant, the sharp images can be obtained by applying a direct inverse filtering method in the spatial domain. Here, inverse filtering is applied to each circular path. Finally, we apply the nonlinear smoothing techniques to enhance the restored images. Experimental results will show the feasibility of the presented blurred image discretization and restoration method.

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For the measurement of the diameter of deformed bars in concrete, an electromagnetic wave (EMW) radar is used which scans along the bar. In our previous method, the radar was run while keeping it in contact with the concrete surface, because this is the usual procedure of scanning with a radar. This resulted in a larger angle of incidence of the EMW to the bar, which consequently elevated the frequency of receiving reflections both from the rib and the base of the bar simultaneously. Therefore, the frequency of erroneous measurement of the propagation time of the EMW to the point on the bar just below the radar and back became large. This consequently greatly affected the success in the measurement of the diameter. Therefore, the present paper proposes a new method. The new method introduces a better scanning procedure, which involves the lift-off of the radar during the scanning. Experiments show the comparison of the successful measurements with and without the lift-off of the radar and verifies the effectiveness of the method.

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The photographs acquired by an optical system are sometimes degraded by relative motion between an imaging system and the original scene during image formation. Traditional methods assume that the relative motion that causes rectilinear smear on the photographs happens at a constant velocity. However, in practical situation, accelerated motion can cause rectilinear smear on the photograph and is the general form of the linear motion. In this paper, we present an analysis of rectilinear smear due to the accelerated motion and the restoration of photographs degraded by the rectilinear smear. The blurred image is restored by using an inverse filter. Experimental results show the feasibility and reliability of the method.

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In this study, the three-dimensional medical image of the cancer of the liver, which is called Hepate-Cellular Carcinoma (HCC), is recognized and extracted by artificial neural network trained using the back propagation algorithm. First, the neural network recognizes the liver regions and the candidate regions of HCC. Then, the density difference image between the early phase image and late phase image of MDCT is extracted. The regions of HCC are detected using the density difference image and the candidate regions of HCC. These image processing are carried out for all slices of MDCT and three-dimensional images of HCC is displayed clearly.

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Geometric hashing method is well-known as one of techniques that realize 3D model matching procedure as quickly as possible. The matching process of the method uses hash-tables prepared off-line for the surface models of all 3D objects to be registered in a database. In order to index the model information into the hash-table, a hash function is required. It has to provide an index value that uniquely describes geometric relations among features extracted from the surface models. In this paper, two hash functions are proposed, in which they are defined by using several geometric features such as normal vectors and curvatures. Furthermore, in order to improve the efficiency of the matching process, a rehashing procedure is introduced so that the calculated indexes may be scattered within the hash table as uniformly as possible. Through experiments using several surface models, it has been verified the geometric hashing method introducing the novel hash functions and the rehashing procedure is effective in 3D object recognition.

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We are developing a pedestrian counter using a multiple number of laser scanners. The occlusion problem can be reduced by using multiple number of horizontally scanning sensors, but the system still suffers from some cases when the number of pedestrians is large. The vertical sensor enforces the capability of signal processing, and also supplements attributes to the detected pedestrians. The detail of the system will be developed.

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This fundamental research is concerned with the crack detection of a concrete pillar combined with a concrete hexahedron, which is a model of the base pile of bridge pier. Stationary waves are generated in the pillar and the hexahedron by hitting the hexahedron with a hammer. An acceleration pickup on the hexahedron observes the stationary waves generated inside the concrete pillar through the hexahedron. The proposed method measures not only the length of the pillar but also the depth of the crack in the pillar by modeling the sensor output as an output of a linear dynamic system with unknown parameters and applying a maximum likelihood method.

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From the viewpoint of the primary criterion “Relationism-First”, it is important to investigate the correlation among environmental factors as many as possible related to utility and risk. So, in this paper, an extended correlation analysis among three environmental factors matched to quantized data distributed within finite intervals is proposed. The effectiveness of the proposed method is experimentally confirmed by applying it to ICT environmental factors (sound, light and EM waves) around a VDT.

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Recently, marginalized particle filter (MPF) has been applied to blind symbol detection problems in wireless systems. MPF is a potential combination of the standard Particle filter and the Kalman filter and can achieve better performance compared with the standard PF in some cases. In this paper, we consider application of the MPF to the problem of blind detection in the presence of the analog imperfections which are inevitable performance degradation factors caused by the imperfection of analog front-end in wireless transceivers. Due to the existence of such impairments, the resulting state-space model of the problem results in non-linear and non-Gaussian and the MPF is not applicable. To cope with this, we employ the auxiliary variable resampling technique to estimate analog imperfection parameters. Simulations are provided that demonstrate the effectiveness of the proposed MPF detector.

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This paper proposes a blind estimation of the fading coefficients without using the pilot symbols in QAM-OFDM systems subjected to carrier frequency offset (CFO) where the phases of the fading coefficients are within ±π/4. First, under a frequency selective fading channel, the inter-carrier interference (ICI) due to CFO is formulated as an ICA model, the permutation and scale uncertainty inherent in ICA is resolved and CFO is estimated. Next, based on the CFO estimation results, the fading coefficients are estimated by use of the fact that symbol constellation at each sub-carrier is stretched/shrunk and rotated according to the value of its fading coefficient. Then, the unknown transmitted symbols are restored by use of the estimated coefficients. Finally, the validity of the proposed approach is confirmed from several simulations for 16QAM-OFDM.

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In this paper a Kalman filter-based detector is developed for signals which are corrupted by nonstationary random noise. The signal detection problem is investigated using the stationarization approach to nonstationary data. The model of the corrupting noise is given by an ARMA(p,q) model with unknown time-varying coefficients. These coefficient parameters are estimated from the (original) observation data by the Kalman filter.

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In [1-3], we have preliminary developed a method of estimating the local models of an ionosphere VTEC (Vertical Total Electron Content) based on GNSS regression models (abbreviated by GR models) and have shown the ionospheric delay (or advance) in the sky over Japan using the Gps Earth Observation NETwork (GEONET) data provided from the Geographical Survey Institute (GSI) of Japan [4]. In this paper, we try to refine the local models based on the orthogonal polynomials for VTEC at the ionospheric pierce points in the ionospheric single layer model with by comparing with the Taylor series expansion. Furthermore from the aspect of model fitting, we discuss the best number of orthogonal polynomials for the local model of VTEC from informational theoretical points of views such as AIC [5] and BIC [6].

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In this paper, we apply nonlinear filtering methods: the Unscented Kalman Filter (UKF) [1] and the Central Difference Kalman Filter (CDKF) [2, 3] to land-vehicle GPS(Global Positioning System)/INS(Inertial Navigation System) integrated navigation systems [4] as well as the In-Motion Alignment systems. Then we show the experimental results of INS/GPS integrated System by using simulated data with assuming the various error sources such as the errors of GPS measurement, INS sensors and various running trajectories.

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The spatial resolution of strain/temperature measurements using Brillouin scattering in an optical fiber is proportional to the pulse width of a pump laser light. However, because the phonon spectrum is broadened and the signal-to-noise ratio (SNR) decreases if the pulse width is narrowed to improve resolution, it was widely assumed that there existed a practical lower limit for pulse width about 10 ns, resulting in resolution of 1 m. In a previous paper, we proposed a spectral broadening suppression method called pulse-prepump Brillouin optical time-domain analysis (PPP-BOTDA), which was verified to attain a 2 cm resolution. In this paper, we apply the pulse compression techniques used in high-resolution radar to increase the SNR of Brillouin distributed sensors, which leads to far higher accuracy.

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Until now, we have studied for the method of the statistical pattern recognition based on auto-regressive (AR) model for the purpose of identifying the EEG signals during motor imagery. The statistical pattern recognition of the EEG signals during three motor imagery (left hand, right hand and right foot) were performed by using the method. As a result, we confirmed that subjects became to able to handle a robot with about a 10 days training. Though, some of subjects were confused to this system since the training system was composed by previous time experiment that included noise element. In this paper, the robust method was introduced to estimate parameter in order to construct more stable BCI system.

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Microarray technology has provided biologists with the ability to measure the expression levels of thousands of genes in a single experiment. One of the urgent issues in the use of microarray data is the selection of a smaller subset of genes from the thousands of genes in the data that contributes to a disease. This selection process is difficult due to many irrelevant genes, noisy genes, and the availability of the small number of samples compared to the huge number of genes (higher-dimensional data). In this study, we propose a three-stage gene selection method to select a smaller subset of informative genes that is most relevant for the cancer classification. It has three stages: 1) pre-selecting genes using a filter method to produce a subset of genes; 2) optimising the gene subset using a multi-objective hybrid method to yield near-optimal gene subsets; 3) analysing the frequency of appearance of each gene in the different near-optimal gene subsets to produce a smaller subset of informative genes. The experimental results show that our proposed method is capable in selecting the smaller subset to obtain better classification accuracies than other related previous works as well as four methods experimented in this work. Additionally, a list of informative genes in the best gene subsets is also presented for biological usage.

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Monochromatic aberrations can limit visual performance of the human eyes. Visual limitations caused by higher-order aberrations can not be corrected by traditional optical correction methods such as spectacles and contact lens. In this paper, we address the problem of correcting visual limitations based on an image deconvolution technique. First, we introduce Zernike polynomials to describe the wavefront aberration. Then, the point spread function (PSF) of the human eyes can be calculated by using the wavefront aberration function. Finally, we propose an image pre-compensation algorithm based on the knowledge of the PSF to improve a blurred image formed by the aberrated eyes. Experimental results are presented to demonstrate the potential visual improvement that can be achived by our pre-compensation algorithm.

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Estimation of brain activity by multivariable autoregressive model is discussed in the paper. We investigate spontaneous changes in the cerebral oxygenation state by using a multi-channel near-infrared spectroscopy: non-invasive optical topography. Hierarchical decomposition analysis [1] is used to estimate a multivariable autoregressive model. The results are viewed by constructing a brain map that normalizes all the subjects.

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In this study, we applied the radial basis function (RBF) neural network to the medical image recognition of the white and gray matters of the brain. This neural network has the three layered architecture that is constructed with the input layer, the hidden layer and the output layer. The regions of the white and gray matters of the brain are recognized and extracted by the RBF neural network and the volumes of these areas are calculated.

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Coupled human balancing tasks are investigated based on the pseudo-neural controller modeled by a time-delayed feedback with a random gain. It is shown numerically that compared with single balancing tasks, a mechanical coupling structure increases stability of balancing errors both in amplitudes and velocities and also improves tracking ability of the controller. We then perform an experiment of replacing the pseudo-neural controller of the numerical model with natural human balancing tasks through the use of computer mouse devices. The result shows that the coupling structure yields asymmetric tracking abilities between the subjects whose tracking abilities are nearly symmetric in their single balancing tasks.

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In this paper, we consider the problem of constructing smoothing spline curves recursively each time when a new set of data is observed. The spline curves are constituted by employing normalized uniform B-splines as the basis functions. Then, based on the basic problem of optimal smoothing splines and an idea of recursive least squares method, a recursive design algorithm of optimal smoothing splines is developed. Assuming that the data for smoothing is obtained by sampling curve, we analyze asymptotical and statistical properties of smoothing spline curve when the number of iterations tends to infinity. The algorithm and analyses are extended to the case of periodic splines. We demonstrate the effectiveness and usefulness by numerical examples.

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In this paper, a stochastic diffusive infectious model in the population consisting of the susceptible and the infective is proposed. We consider the proliferation with the strong Allee effect, which means that there exists the optimal population density maximizes the per capita proliferation rate and it becomes negative at the low population density. By numerical simulations, we show that spatio-temporal patterns of the epidemic spreading process become the fractal structure like the Sierpinski gasket in some restricted parameter range and the patterns under the noise are very different from ones in the no noise case in the other restricted parameter range.

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Physical, chemical and social phenomena contain some kind or another of uncertainties to a greater or lesser extent. The analysis of influence of such uncertainties on phenomena is very important as a basic problem in various fields including design and planning of controlled systems in control engineering and analysis of option pricing in economics. In this paper, focusing on biological communities, we study the influence of the random uncertainties on predator-prey systems with diffusion. Noting that interaction of phytoplankton and zooplankton is the basis of a food chain in the ocean, we firstly consider the stochastic predator-prey systems consists of phytoplankton and zooplankton. Secondly, a modeling of the stochastic phytoplankton-zooplankton-fish system is considered. We analyze the influence of the random uncertainties on the spatio-temporal patterns generated by two types of the predator-prey systems with diffusion by the numerical simulations.

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Nonlinear systems described by the simple mathematical model often exhibit extremely complicated behavior called chaos. In this paper, chaotic behavior, exhibited by the one-dimensional difference equation, is discussed. A class of nonlinear discrete system with the invariant density, which is multi step type piece-wise uniform, is newly introduced.

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Nonlinear oscillators including chaotic systems are very important devices, and furthermore it is one of essential component in the natural world to solve a mechanism of a nonlinear dynamics in several networks. In this study, a simple chaotic circuit with three states of both chaotic oscillation and two different size limit cycles which is called Multi-State Chaotic Circuit (MSCC) is proposed. Synchronization phenomena and complex behavior on a simple network system of the MSCCs coupled by some inductors are investigated. Several interesting chaotic phenomena of phase synchronization behavior have been observed in the coupled network system.

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