Control of chaos: Methods and applications in engineering

The problems and methods of control of chaos, which in the last decade was the subject of intensive studies, were reviewed. The three historically earliest and most actively developing directions of research such as the open-loop control based on periodic system excitation, the method of Poincare map linearization (OGY method), and the method of time-delayed feedback (Pyragas method) were discussed in detail. The basic results obtained within the framework of the traditional linear, nonlinear, and adaptive control, as well as the neural network systems and fuzzy systems were presented. The open problems concerned mostly with support of the methods were formulated. The second part of the review will be devoted to the most interesting applications.

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Control of Chaos: Methods and Applications. I. Methods

Associative memory with a controlled chaotic neural network

Real-time deterministic chaos control by means of selected evolutionary techniques

This paper investigates the complex dynamics, synchronization and control of chaos in a system of strongly connected Wilson{Cowan neural oscillators. Some typical synchronized periodic solutions are analyzed by using the Poincar e mapping method, for which bifurcation diagrams are obtained. It is shown that topological change of the synchronization mode is mainly caused and carried out by the Neimark{Sacker bifurcation. Finally, a simple feedback control method is presented for stabilizing an in-phase synchronizing periodic solution embedded in the chaotic attractor of a higher-dimensional model of such coupled neural oscillators.

/pdf/on-synchronization-and-control-of-coupled-wilson-cowan-31zd96e9av.pdf

On synchronization and control of coupled wilson cowan neural oscillators

We propose how to control chaos in chaotic neural networks. We show that chaos in simple chaotic neural networks, which were proposed by K. Aihara et al., can be controlled under either global or nearest neighbor coupling. The proposed method is based on exponential feedback control as proposed by S. D. Gadre and V. S. Varma. Exponential feedback control makes one of the unstable periodic orbits stable using multiplicative exponential feedback on a system parameter. Their method allows the system to diverge when the feedback becomes too large, and it is impossible to select a desired point from several periodic points at any given time. We extend this method to limit feedback so that the system will not diverge. We also make the exponential term for feedback dependent on each desired point. These extensions enable us to control chaos even when the system is far from the desired orbit, and enable us to select any desired point at any given time.

Controlling chaos in chaotic neural networks

Controlling Chaos in Chaotic Neural Networks

We show by numerical calculations that a chaotic neuron model driven by a weak sinusoid has resonance. This resonance phenomenon has a peak at a drive frequency similar to that of noise-induced stochastic resonance (SR). This neuron model was proposed from biological studies and shows a chaotic response when a parameter is varied. SR is a noise induced effect in driven nonlinear dynamical systems. The basic SR mechanism can be understood through synchronization and resonance in a bistable system driven by a subthreshold sinusoid plus noise. Therefore, background noise can boost a weak signal using SR. This effect is found in biological sensory neurons and obviously has some useful sensory function. The signal-to-noise ratio (SNR) of the driven chaotic neuron model is improved depending on the drive frequency; especially at low frequencies, the SNR is remarkably promoted. The resonance mechanism in the model is different from the noise-induced SR mechanism. This paper considers the mechanism and proposes possible explanations. Also, the meaning of chaos in biological systems based on the resonance phenomenon is considered. key words: driven chaotic system, chaotic neuron model, biological information processing, stochastic resonance, numerical calculation

Resonance in a Chaotic Neuron Model Driven by a Weak Sinusoid

PURPOSE: To obtain a correlative dimension and a Liapunov spectrum even from quasi-stationary time series data consisting of a combination of stationary time sections CONSTITUTION: A spectrum Pt0 (f) at a time t0 and a spectrum pt (f) at a time(t) for time series data x(t) (S1) are calculated (S2), and spectrum error quantity is used as a measure for the difference of them (S3) When the spectrum error quantity over a threshold value is detected (S4), segmentation is performed adaptively assuming a time until then as t1 and a stationary time section as T1 (S5) After that, an attractor is reconfigured by an embedding method for the time section T1 (S6), and hereinafter, the correlative dimension of the time section is found similarly as in a conventional method The correlative dimension is found from the quasi-stationary time series data consisting of the combination of the stationary time sections

Method and device for correlative dimension analysis, and method and device for liapunov spectrum analysis, for quasi-stationary time series using adaptive segmentation

PROBLEM TO BE SOLVED: To enable detecting a fine periodic signal, by amplifying a periodic signal having a specific frequency, and judging the frequency of the periodic signal from a peak value detected from an amplified chaos time series. SOLUTION: By a signal input circuit 1, a very fine periodic signal is inputted in a chaos neurone circuit 2 in which the dynamics of a neurone model capable of forming chaos is realized by electric circuits. A fine periodic signal inputted by the resonance phenomenon is amplified, and stored 3 in a time series. A frequency analyzing circuit 4 calculates and outputs frequency distribution, from the amplified chaos time series. A peak detecting circuit 5 compares relatively the calculated 4 frequency distribution, detects a peak of frequency, and judges the frequency of the periodic signal. Thereby, a very fine periodic signal can be detected.

Signal detecting method and equipment using chaos neurone model

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