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Abstract: The concept of deterministic chaos has been making large impacts both on science and on engineering. Possible applications of chaotic dynamics are considered from a viewpoint of chaos engineering. [Copyright &y& Elsevier]

Here we demonstrate a computing system employing an amoeba of a true slime mold Physarum known as a model organism for studying cellular information processing. The system works as a neurocomputer that exhibits high optimization capability in solving various problems including the traveling salesman problem. Additionally, we present a new technique that we call "autonomous meta-problem solving." In this approach, our system not only can solve a given problem but also can find new problems and then determine solutions by exploiting the amoeba's unique searching ability and spontaneous behavior. [ABSTRACT FROM AUTHOR]

A widely used complex-valued activation function for complex-valued multistate Hopfield networks is revealed be essentially based on a multilevel step function. By replacing the multilevel step function with other multilevel characteristics, we present two alternative complex-valued activation functions. One is based on a multilevel sigmoid function, while the other on a characteristic of a multistate bifurcating neuron. Numerical experiments show that both modifications to the complex-valued activation function bring about improvements in network performance for a multistate associative memory. The advantage of the proposed networks over the complex-valued Hopfield networks with the multilevel step function is more outstanding when a complex- valued neuron represents a larger number of multivalued states. Further, the performance of the proposed networks in reconstructing noisy 256 gray-level images is demonstrated in comparison with other recent associative memories to clarify their advantages and disadvantages [ABSTRACT FROM AUTHOR]

The bifurcation structure of a constraint Duffing van der Pol oscillator with a diode is analyzed and an objective bifurcation diagram is illustrated in detail in this work. An idealized case, where the diode is assumed to operate as a switch, is considered. In this case, the Poincaré map is constructed as a one-dimensional map: a circle map. The parameter boundary between a torus-generating region where the circle map is a diffeomorphism and a chaos-generating region where the circle map has extrema is derived explicitly, without solving the implicit equations, by adopting some novel ideas. On the bifurcation diagram, intermittency and a saddle-node bifurcation from the periodic state to the quasi-periodic state can be exactly distinguished. Laboratory experiment is also carried out and theoretical results are verified. [ABSTRACT FROM AUTHOR]

Chaotic neurons are interconnected with each other through a matrix of dynamic synaptic weights to constitute an associative network. First, the dynamics of the two chaotic neurons connected with dynamic synapses is analyzed. A quick memory switching phenomenon in the Associative Network with Chaotic Neurons and Dynamic Synapses (ANCNDS) is then demonstrated. It is further discovered that the memory retrieval frequency of the network among stored patterns distributes more uniformly, and is much higher than that of a chaotic network without dynamic synapses. Moreover, the network acts as a peculiar pattern recognition system when applied with external stimulations. If the external stimulation is close to only one stored pattern, the network recalls the stored pattern exactly. On the other hand, if the external stimulation shares similarity with two or several stored patterns, the network transits among these related stored patterns. When the external stimulation does not resemble any stored patterns, the network wanders among all the stored patterns. [ABSTRACT FROM AUTHOR]

We propose a simple neural network model to understand the dynamics of temporal pulse coding. The model is composed of coincidence detector neurons with uniform synaptic efficacies and random pulse propagation delays. We also assume a global negative feedback mechanism which controls the network activity, leading to a fixed number of neurons firing within a certain time window. Due to this constraint, the network state becomes well defined, and the dynamics equivalent to a piecewise nonlinear map. Numerical simulations of the model indicate that the latency of neuronal firing is crucial to the global network dynamics; when the timing of postsynaptic firing is less sensitive to perturbations in timing of presynaptic spikes, the network dynamics become stable and periodic, whereas increased sensitivity leads to instability and chaotic dynamics. Furthermore, we introduce a learning rule which decreases the Lyapunov exponent of an attractor and enlarges the basin of attraction. [ABSTRACT FROM AUTHOR]

Using the wavelet transform, we can express a time series as a summation of frequency components each of which is localized in the frequency domain. In the present paper, we show that each frequency component given as the wavelet coefficients of a deterministic time series preserves the topological structure of the original dynamical system. We subsequently propose new methods to predict a time series by applying the inverse wavelet transform to predictees of frequency components. Our methods can realize good long-term predictions of deterministic time series contaminated with either high-frequency deterministic noise or white noise. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(6): 50–59, 2001 [ABSTRACT FROM AUTHOR]

A learning algorithm is introduced for chaotic dynamical systems that solve nonlinear optimization problems. The algorithm controls the asymptotic measure of a chaotic dynamical system that searches for the optimum solution and improves the efficiency of chaotic search dynamics. Using several instances of 1- and 2-dimensional nonlinear optimization problems, the performance of the learning algorithm is demonstrated. We also show that the learning algorithm works as chaotic simulated annealing, which brings about gradual convergence of the chaotic search dynamics to a possible optimum solution. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(3): 10–21, 1999 [ABSTRACT FROM AUTHOR]

A fully local algorithm which can automatically detect and learn an unknown pattern is proposed for a mutually connected recurrent neural network, and its fundamental properties are numerically analyzed. The algorithm is applied to chaotic neural networks composed of neuron models with spatiotemporal inputs and refractoriness and to conventional mutually connected neural networks. It is shown that the former could learn more patterns with greater robustness than the latter. [ABSTRACT FROM AUTHOR]

We apply a TDOF (two-degree-of-freedom) robust controller to chaotic dynamical systems. We show that the TDOF controller is effective not only for rejection of chaotic disturbance but also for control of a chaotic plant. [ABSTRACT FROM AUTHOR]

This paper presents a global bifurcation scenario for chaotic dynamical systems that solve optimization problems. First, a chaotic dynamical system is constructed by a discretization of the gradient-descent dynamical system of the objective function. With an increase in the discretization parameter, local minimum solutions of the objective function bifurcate into chaotic attractors through a period-doubling bifurcation. The chaotic attractors are initially localized in the state space and eventually merge into a single global chaotic attractor via a series of crises. On the global chaotic attractor which visits a variety of local minima, “chaotic search” for a global minimum is realized. On the basis of the bifurcation scenario, we provide a guideline for tuning the bifurcation parameter value which gives rise to an efficient “chaotic search.” We also consider the efficiency of the “chaotic simulated annealing” algorithm in the light of its annealing schedule. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(2), 1–12, 1998 [ABSTRACT FROM AUTHOR]

The two-link nozzle in the dishwater-dryer is composed of two links which rotate by the water flow. Although the behavior of the two-links nozzle is related closely to the washing performance of the dishwasher, its behavior is complex. In this sense, in order to improve the washing performance of the dishwater, it is necessary to analyze the behavior of the two-link nozzle and to clarify the washing mechanism. This study aims at providing the basis for the analysis of the behavior of the two-link nozzle. The motion of the nozzle is detected by image processing, and the behavior of the nozzle is analyzed based on the derived time-series from the viewpoint of the deterministic chaos. The result is reported. [ABSTRACT FROM AUTHOR]

A one-dimensional mapping of a chaotic neuron model which generates deterministic chaos is analyzed from the viewpoint of the information theory. First, the mutual information between the initial value and the value after iterations of the mappings is calculated, and it is shown that the information of the initial value decays almost exponentially. To examine the decaying behavior in detail, the dynamics of the chaotic neuron model is represented as the information flow of‘0’and‘1’in a bitwise space (register) and the behavior of the mutual information contained in each bit is examined. It is shown through this analysis that the information in the chaotic neuron model is maintained, being mixed and distributed among the hits. Moreover, the chaotic neuron model is compared with two typical chaotic dynamical systems with different information structures, i.e., the B-Z mapping and the logistic mapping to clarify the information structure. Finally, it is shown for the system, where the chaotic neuron models are unidirectionally connected as a one-dimensional network, that the information transmission is made possible by its peculiar information structure. [ABSTRACT FROM AUTHOR]

A technique for forecasting daily peak load in a utility power system is presented. After embedding time series data of daily peak load into a reconstructed state space, a nonlinear mapping is constructed by a local approximation method based on the orthonormal Gram-Schmidt bases. This method utilizes only the past load data for short-term prediction of the daily peak load, while many conventional methods make predictions with various kinds of data such as temperature and weather. The quality of prediction by the proposed method is as good as those with other prediction methods. Moreover, the results of short-term prediction by this method are satisfactory even with data as small as 250 points. [ABSTRACT FROM AUTHOR]

Abstract: In hybrid dynamical systems including both continuous and discrete components, an interplay between a continuous trajectory and a discontinuity boundary can trigger a sudden qualitative change in the system dynamics. Grazing phenomena, which occur when a continuous trajectory hits a boundary tangentially, are well known as a representative of such phenomena. We demonstrate that a grazing phenomenon of a chaotic attractor can result in its sudden disappearance and initiate chaotic transients. The mechanism of this grazing-induced crisis is revealed in an illustrative example. Furthermore, we derive a formula to obtain the critical exponent of the power law on the mean duration of chaotic transients. [Copyright &y& Elsevier]

Abstract: Two coexisting stable canards are discussed in a periodically driven singularly perturbed van der Pol equation, where the amplitude of the driving force is extremely small. Canard breakdown into chaos via period-doubling bifurcations is also observed. [Copyright &y& Elsevier]

Abstract: We propose an asynchronous spiking chaotic neuron circuit for temporal coding networks based on coincidence detection and spatio-temporal chaotic dynamics. In the proposed circuit, we take into account the coincidence detection among input spikes, continuous-time interspike intervals, relative and absolute refractoriness, an analog internal state value, a continuous output function, an output spike generation delay, and synaptic weight. We implement the neuron circuit with a 0.5 m CMOS semiconductor process by means of analog circuitry. Moreover, we make most of the model parameters externally controllable so that we can control the behavior of the neuron. As a consequence, by properly setting its circuit parameters, the neuron can function as either a coincidence detector or an integrator. We show the measurement results from the prototype chip. In particular, we show coincidence detection of the input spikes in a short time-window. In addition, we illustrate complex responses of the neuron circuit, providing bifurcation diagrams of the internal state value and the interspike intervals of the output spikes. The proposed neuron circuit is useful for exploring a possible spatio-temporal coding paradigm by constructing a neural network based on the coincidence detection and the spatio-temporal chaotic dynamics. [Copyright &y& Elsevier]

Abstract: Hybrid systems are widely used to model dynamical phenomena that are characterized by interplay between continuous dynamics and discrete events. An example of biomedical application is modeling of disease progression of prostate cancer under intermittent hormonal therapy, where continuous tumor dynamics is switched by interruption and reinstitution of medication. In the present paper, we study a hybrid systems model representing intermittent androgen suppression (IAS) therapy for advanced prostate cancer. Intermittent medication with switching between on-treatment and off-treatment periods is intended to possibly prevent a prostatic tumor from developing into a hormone-refractory state and is anticipated as a possible strategy for delaying or hopefully averting a cancer relapse which most patients undergo as a result of long-term hormonal suppression. Clinical efficacy of IAS therapy for prostate cancer is still under investigation but at least worth considering in terms of reduction of side effects and economic costs during off-treatment periods. In the model of IAS therapy, it depends on some clinically controllable parameters whether a relapse of prostate cancer occurs or not. Therefore, we examine nonlinear dynamics and bifurcation structure of the model by exploiting a numerical method to clarify bifurcation sets in the hybrid system. Our results suggest that adjustment of the normal androgen level in combination with appropriate medication scheduling could enhance the possibility of relapse prevention. Moreover, a two-dimensional piecewise-linear system reduced from the original model highlights the origin of nonlinear phenomena specific to the hybrid system. [Copyright &y& Elsevier]