Since A. M. Turing introduced the notion of computability in 1936, various theories of real number computation have been studied [1, 10, 13]. Some are of interest in nonlinear and statistical physics while others are extensions of the mathematical theory of computation. In this review paper, we introduce a recently developed computability theory for Julia sets in complex dynamical systems by Braverman and Yampolsky [3].

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For a class of vector fields, we show that one can selectively average terms which are of the same order in a small parameter, giving an extension of standard averaging results. Such selective averaging is illustrated for the phase reduction of a system of oscillators with both coupling and external input, for which the coupling can be averaged to give a term which only depends on phase differences, while the external input term is not averaged. For a coupled two-neuron system, we use selectively averaged equations to find the optimal input which takes the in-phase state to the anti-phase state.

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We numerically investigate multiple basins of consistency in the Mackey-Glass model driven repeatedly by a colored noise signal. The Mackey-Glass model is modified to include the saturation effect for the observation of multiple basins of consistency. Consistent response outputs are obtained for strong drive strength, whereas no consistency is observed for small drive strength. For intermediate drive strength, more than one type of consistent response waveforms can be observed, known as multiple basins of consistency. The regions of multiple basins are entangled in the phase space. The number of multiple basins of consistency depends on the drive strength and the saturation threshold in the Mackey-Glass model. Our findings are confirmed experimentally by using an electronic circuit of the Mackey-Glass model with a colored-noise drive signal.

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This paper presents a novel application of an operational transconductance amplifier configuration for implementing the basic logic gates using the concept of stochastic resonance (SR). In such framework, the SR effect applied to nonlinear electrical systems to build logical gates (SR gates) has been studied. The property of hysteresis is crucial: first, it reduces the error rate regarding mismatch problems with cooperative use of noise, and second, it ensures the stability of all logic states. However, in this configuration, the toggles exhibit an unpredictable delay, which has been reviewed in this study; therefore, the most suitable application of the SR gates is in asynchronous circuit design. Circuit performance was electrically simulated using SPICE for 0.18-µm CMOS technology. The simulation results have proven the effective performance of the SR gates for an optimal amount of noise working at low power consumption, despite the introduction of an intentional mismatch between the threshold voltages of the transistors.

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We demonstrate a possible application of “steganography” in a reaction-diffusion (RD) cellular automata (CA) model toward digital hardware (HW) implementation. Steganography is one of data-hiding techniques which conceal hidden data transmitted between the sender and receiver. Recently, a new steganography algorithm based on self-organizing patterns which are generated by a prey-predator model was proposed. However, this model has rich nonlinearity which complicates the HW implementation. Therefore, in this paper, we demonstrate numerical simulations of the RD steganography using the RD CA model which has simple dynamics and generates striped or spotted patterns. Obtained results indicate that the RD CA model is suitable for HW implementation of RD steganography.

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Because of an increasing demand on electric power and limited resources for conventional fuels, highly efficient engine that is capable of converting energy resource to electric power with a small loss is awaited. In this respect, Stirling engine provides a strong potential because of its efficient thermodynamic cycle, which is ideally close to the theoretical limit of the Carnot cycle. Practical use of the Stirling engine, however, has been limited because of its low output power. Towards its wider applicability, simultaneous operation of many individual Stirling engines is indispensable to increase the output power. This paper presents an experimental study of synchronized dynamics of two coupled Stirling engines. It is shown that the synchronized operation of the population of engines provides a key technology to extend the system size so as to produce a large-scale electric energy.

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In this paper, we discuss to control of the number of clusters formed by distributed robots only with local information. This work was motivated by Swiss Robots, which collect scattered obstacles into some clusters without any global information nor intelligent concentrated controller. In this paper, we define fundamental event rules in this cellular world, and introduce two types of local rules for robot action: one is the Push & Turn rule, which can collect obstacles, the other is Pull & Turn rule, which can scatter obstacles. First, we show that the number of clusters can be estimated based on intrinsic memory of individual agents. Then, we propose a “mode switching strategy” that a robot is autonomously switching 4 modes: core-creating/growing/estimating, and fracturing mode. Repeated trials indicate that we can statistically control of the number of clusters by adjusting the switching threshold. And, we also show that timely switching between two rules in core-creating mode achieves to form a single cluster. At last, we describe that introducing anisotropic robots will lead to shift a clustering position.

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In this paper, we discuss some phenomena of distributed transportation inspired by the foraging behavior of ants, in the light of space-discretization (or cellular automata) approach. We define fundamental event rules in a cellular world, and introduce two types of ant agents: one is an oriented ant, which perceives pheromones; the other is a random ant, which does not perceive pheromones. We then take a closer look at the number of pheromone trails formed by homogeneous and heterogeneous agents. Moreover, we propose a distributed control method for the number of formed pheromone trails, and examine the effectiveness of the proposed method in several simulations.

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We report, in this paper, a highly efficient CMOS rectifier for low power energy harvesting system. By using full bridge structure and a novel active diode, the rectifier can work at a wide range of input voltage amplitudes of 0.45V up to 1.8V under a standard 0.18µm CMOS process. A comparator that consists of common-gate stage and control stage is designed to control the switch of the active diode. The proposed rectifier can achieve a peak voltage conversion efficiency of over 96% and a power efficiency over 90%. Simulated power consumption of the rectifier is 264.35nW at 500mV, which is much smaller than the best recently published results.

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Pseudo-transient analysis, PTA, method is regarded as a practical method to find DC operating points of nonlinear circuits when the Newton-Raphson method fails. However, the convergence and efficiency of the previous studies are not satisfactory. Moreover, the numerical examples of previous studies are mainly for small-scale circuits or single type of circuits. Therefore, finding a more practical pseudo-transient analysis method for large-scale circuits and complex circuits becomes necessary and important. This paper proposes a new PTA method using numerical integration algorithms with artificial damping, and proposes a switching method in the implementation as well. The mathematical descriptions of the numerical integration algorithms are presented. The efficiency of the proposed PTA method is illustrated by solving practical nonlinear circuits.

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This paper studies the collision particle swarm optimizer (CPSO) for discrete multi-solution problems (DMSP). The dynamics of the CPSO is governed by a deterministic difference equation on a discrete search space. It is useful from viewpoints of reproducibility and implementation. The CPSO can use inter-particle collision that can be effective to avoid trapping into partial/local solutions. The CPSO is applied to a DMSP based on an exploring problem of periodic points of the Hénon map. Performing elementary numerical experiments, the basic capability of the CPSO is investigated. This application is the first step to develop PSO-based analysis tool of nonlinear dynamical systems.

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This paper studies a hyperchaotic spiking circuit that consists of a three-dimensional linear one-port, a state-dependent switch, and a time-dependent switch. The two switches are connected in series. Depending on parameters, the circuit can exhibit various spike-trains. In order to analyze the spike-trains, we introduce three tools: the return map, the histogram of inter-spike intervals, and the color recurrence plot of spike-trains. Using the tools, we analyze three typical phenomena: a periodic spike-train, a chaotic spike-train, and a hyperchaotic spike-train. Presenting a simple test circuit, the typical phenomena are confirmed experimentally.

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