The 20th NOLTA Symposium, the 2010 International Symposium on Nonlinear Theory and Its Applications, was held successfully in Krakow, Poland, during September 5-8, 2010. This special issue has been planned in order to encourage, in particular but not restricted to, the authors who presented their nice works at NOLTA 2010 to submit their recent works to NOLTA, IEICE. Through the standard blind review process of NOLTA, 15 excellent papers are selected for this special issue. The guest editor would like to thank all of the authors for their contributions. He also thanks the reviewers and the guest editorial committee members for their supports on the review process. Finally, he would like to express his sincere appreciation of the hard work on this special issue to Dr. Uwate, the guest secretary. Enjoy reading the papers in this special issue.
This paper presents an analysis of delay-locked loops in direct spreading code division multiple access systems with Markovian spreading sequences. The established analysis with piecewise constant approximation is similar to the mean field analysis which estimates macroscopic characteristics of a spatially-distributed probabilistic system from the local interaction between the elements of the system with low computational complexity. The low complexity makes it possible to analyze the behavior of not only second-order archetype delay-locked loops but also higher-order non-coherent delay-locked loops in the presence of both multiple access interference and channel noise. It is found from the presented analysis that replacing i.i.d. spreading sequences with Markovian spreading sequences with non-vanishing negative autocorrelation reduces the phase tracking error of a non-coherent 1Δ delay-locked loop. The time spent for estimating the error by the presented method is about 1/1000 compared with that by the path integral method.
This paper presents a way to cope with the need of simultaneously rejecting narrowband interference and multi-access interference in a UWB system based on direct-sequence CDMA. With this aim in mind, we rely on a closed-form expression of the system bit error probability in presence of both effects. By means of such a formula, we evaluate the effect of spectrum shaping techniques applied to the spreading sequences. The availability of a certain number of degrees of freedom in deciding the spectral profile allows us to cope with different configurations depending on the relative interfering power but also on the relative position of the signal center frequency and the narrowband interferer.
We give a novel lower bound of the minimum values of the normalized auto-correlation functions for de Bruijn sequences of length N=2n(n≥3). The lower bound is tight in the sense that the equality holds for n=3 and n=4. For 3≤n≤6, we experimentally characterize the worst and the second-worst sequences in all de Brujin sequences in terms of the normalized auto-correlation function.
In this paper, we demonstrate stochastic resonance (SR) in a double-well potential system that can easily be implemented by a single operational amplifier. First, we propose a bistable mathematical model that is suitable for analog hardware implementation. Then we introduce an analog circuit for the model that is implemented by a single operational amplifier only, and demonstrate that the circuit exhibits the same SR behavior demonstrated in traditional double-well potential systems, through extensive numerical simulations and experiments.
Burst firing dynamics that are observed in many neuron models including the Hodgkin-Huxley model, are explained in terms of a motion of a quasi particle bound by potential. We are able to foresee the solution landscape with the curvature of the potential, and can design the wave form of the output to properly set active areas on the potential. In this paper, we apply this concept for a single Hindmarsh-Rose model and a coupled van der Pol oscillators. Therefore, we provide an understanding of the burst firings with spatiotemporal constructions of the potential and the active areas, and claim that the active areas cause the eigen-oscillations individually. Hence, we dispose the active areas on the potential properly and design the intended wave forms. Then, the global curvature of the potential function ensures that these oscillations do not diverge.
Global asymptotic stability of the nonlinear circuit similar to the one proposed by Sato et al. for solving the maximum flow problem is studied in this paper. The circuit consists of two independent DC voltage sources, capacitors and nonlinear resistors. It is proved rigorously that the circuit has a unique equilibrium point which is globally asymptotically stable. From the viewpoint of dynamical systems, the circuit is a cooperative system, and thus some fundamental results concerning the convergence property of cooperative systems play important roles.
The clustering coefficient is one of the most important quantities characterizing complex networks. It is often said that many networks in the real world have high clustering coefficients. However, properties of the clustering coefficient itself have not been discussed much in the literature. In this paper, some fundamental properties of the clustering coefficient are studied. First we try to find the maximum value of the clustering coefficient of graphs with the given number of vertices and edges. Next we present some classes of graphs such that each member maximizes the clustering coefficient among its neighbors having the same number of vertices and edges.
This paper proposes an application of the particle swarm optimization (PSO) to analysis of switched dynamical systems (SDS). This is the first application of PSO to bifurcation analysis. We consider the application to an example of the SDS which relates to a simplified model of photovoltaic systems such that the input is a single solar cell and is converted to the output via a boost converter. Our SDS includes a piecewise linear current-controlled voltage source that is a simplified model of the solar cell and the switching rule is a variant of peak-current-controlled switching. We derive two equations that give period-doubling bifurcation set and the maximum power point (MPP) for the parameter: they are objective of the analysis. The two equations are transformed into an multi objective problem (MOP) described by the hybrid fitness function consisting of two functions evaluating the validity of parameters and criteria. The proposed method permits increase (deteriorate) of some component below the criterion and the increase can help to exclude the bad component. This criteria effect helps an improvement of trade-off problems in existing MOP solvers. Furthermore, by using the piecewise exact solution and return map for the simulation, the MOP is described exactly and the PSO can find the precise (approximate) solution. From simulation results, we confirm that the PSO for the MOP can easily find the solution parameters although a standard numerical calculation needs huge calculation amount. The efficiency of the proposed algorithm is confirmed by measuring in terms of accuracy, computation amount and robustness.
The quadratic assignment problem (QAP) is one of the NP-hard combinatorial optimization problems. An exponential chaotic tabu search using a 2-opt algorithm driven by chaotic neuro-dynamics has been proposed as one heuristic method for solving QAPs. In this paper we first propose a new local search, the double-assignment method, suitable for the exponential chaotic tabu search, which adopts features of the Lin-Kernighan algorithm. We then introduce chaotic neuro-dynamics into the double-assignment method to propose a novel exponential chaotic tabu search. We further improve the proposed exponential chaotic tabu search with the double-assignment method by enhancing the effect of chaotic neuro-dynamics.
Chaotic dynamics has been shown to be effective in improving the performance of combinatorial optimization algorithms. In this paper, the performance of chaotic dynamics in the asymmetric traveling salesman problem (ATSP) is investigated by introducing three types of heuristic solution update methods. Numerical simulation has been carried out to compare its performance with simulated annealing and tabu search; thus, the effectiveness of the approach using chaotic dynamics for driving heuristic methods has been shown. The chaotic method is also evaluated in the case of a combinatorial optimization problem in the real world, which can be solved by the same heuristic operation as that for the ATSP. We apply the chaotic method to the DNA fragment assembly problem, which involves building a DNA sequence from several hundred fragments obtained by the genome sequencer. Our simulation results show that the proposed algorithm using chaotic dynamics in a block shift operation exhibits the best performance for the DNA fragment assembly problem.
Chaotic dynamics have been effectively applied to improve various heuristic algorithms for combinatorial optimization problems in many studies. Currently, the most used chaotic optimization scheme is to drive heuristic solution search algorithms applicable to large-scale problems by chaotic neurodynamics including the tabu effect of the tabu search. Alternatively, meta-heuristic algorithms are used for combinatorial optimization by combining a neighboring solution search algorithm, such as tabu, gradient, or other search method, with a global search algorithm, such as genetic algorithms (GA), ant colony optimization (ACO), or others. In these hybrid approaches, the ACO has effectively optimized the solution of many benchmark problems in the quadratic assignment problem library. In this paper, we propose a novel hybrid method that combines the effective chaotic search algorithm that has better performance than the tabu search and global search algorithms such as ACO and GA. Our results show that the proposed chaotic hybrid algorithm has better performance than the conventional chaotic search and conventional hybrid algorithms. In addition, we show that chaotic search algorithm combined with ACO has better performance than when combined with GA.
In this paper, we report a way to store color images in a large-scale chaotic neural network and to retrieve them by using chaotic dynamics. In the proposed method, color images are converted to binary codes, modified slightly by inverting a few bits, and stored in the network. The results of numerical simulations show that chaotic transitions among stored patterns and their reverse patterns can be observed within a certain range of parameters. We also compare five different coding schemes of color information, which change the appearance of chaotic dynamics. In addition, if connections are restricted in a neighborhood of each unit, a variety of wave patterns are observed.
This paper presents a novel architecture for an FPGA-based implementation of multilayer Artificial Neural Network (ANN), which integrates both the layer-multiplexing and pipeline architecture. Given a kind of FPGA to be used, the proposed method aims at enhancing the efficiency of resource usage of the FPGA and improving the forward speed at the module level, so that a larger ANN can be implemented on traditional FPGAs and also a high performance is achieved. Usually FPGA board is not changed for every applications, thus, we need not mind about the usage of it if the application can be implemented within the resource limitation. We developed a new mapping method from ANN schematic to FPGA by using this hybrid architecture, and also developed an algorithm to automatically determine the architecture by optimizing the application specific neural network topology. The experimental results show that the proposed architecture can produce a very compact circuit for multilayer ANN to meet resource limitation of a given FPGA. Furthermore, higher performance is obtained as compared with conventional methods.
In this paper, we develop a new approach based on discrete mechanics to a gait generation problem for the compass-type biped robot. First, both continuous-time and discrete-time models of the compass-type biped robot are derived. We next formulate a discrete gait generation problem for the discrete compass-type biped robot as a finite dimensional nonlinear optimal control problem and show an algorithm to solve the problem based on the sequential quadratic programming. Then, we propose a transformation method that converts a discrete-time control input into a continuous-time zero-order hold one and apply it to gait generation for the continuous compass-type biped robot. Some simulations are also shown in order to verify the effectiveness of our new approach.
In this paper we propose a numerical method to extract the four parameters (Ro, R∞, C, and α) that characterize a single-dispersion Cole-Cole impedance model from its step response, based on modelling the step response using fractional calculus, without requiring direct measurement of the real and imaginary impedance parts. MATLAB simulations using Cole-Cole impedances of fruit tissues with α<1, PSPICE simulations and experimental results using a Cole-Cole model with α=1 are given to verify the method. Extracted impedance parameters show less than 0.1% relative error in simulation and less than 10% error in experimental results for the extracted impedance parameters.