Observation of Strange Nonchaotic Dynamics in the Frame of State-Controlled Cellular Neural Network-Based Oscillator

Abstract In this paper, the strange nonchaotic dynamics of a quasi-periodically driven state-controlled cellular neural network (SC-CNN) based on a simple chaotic circuit is investigated using hardware experiments and numerical simulations. We report here two different routes to strange nonchaotic attractors (SNAs) taken by this SC-CNN based circuit system. These routes were confirmed using rational approximation (RA) theory, finite time Lyapunov exponents, spectrum of the largest Lyapunov exponents and their variance, and phase sensitivity exponent. It is observed that the results from both computer simulations as well as laboratory experiments have spectacular resemblance.

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A New Route to Strange Nonchaotic Attractors in an Interval Map

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420500637 ◽

2020 ◽

Vol 30 (04) ◽

pp. 2050063 ◽

Cited By ~ 2

Author(s):

Yongxiang Zhang ◽

Yunzhu Shen

Keyword(s):

Lyapunov Exponents ◽

Control Parameter ◽

Power Spectra ◽

Phase Sensitivity ◽

Recurrence Analysis ◽

Grazing Bifurcation ◽

Remarkable Feature ◽

Finite Time Lyapunov Exponents ◽

Interval Map ◽

Strange Nonchaotic Attractors

We identify an unusual route to the creation of a strange nonchaotic attractor (SNA) in a quasiperiodically forced interval map. We find that the smooth quasiperiodic torus becomes nonsmooth due to the grazing bifurcation of the torus. The nonsmooth points on the torus increase more and more with the change of control parameter. Finally, the torus gets extremely fractal and becomes a SNA which is termed the grazing bifurcation route to the SNA. We characterize the SNA by maximal Lyapunov exponents and their variance, phase sensitivity exponents and power spectra. We also describe the transition between a torus and a SNA by the recurrence analysis. A remarkable feature of the route to SNAs is that the positive tails decay linearly and the negative tails exhibit recurrent fluctuations in the distribution of the finite-time Lyapunov exponents.

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Coexistence of Strange Nonchaotic Attractors in a Quasiperiodically Forced Dynamical Map

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420501837 ◽

2020 ◽

Vol 30 (13) ◽

pp. 2050183

Author(s):

Yunzhu Shen ◽

Yongxiang Zhang ◽

Sajad Jafari

Keyword(s):

Power Spectrum ◽

Lyapunov Exponents ◽

Basins Of Attraction ◽

Initial Condition ◽

Phase Sensitivity ◽

Coexisting Attractors ◽

Sensitive Dependence ◽

Largest Lyapunov Exponents ◽

The Creation ◽

Strange Nonchaotic Attractors

In this paper, we investigate coexisting strange nonchaotic attractors (SNAs) in a quasiperiodically forced system. We also describe the basins of attraction for coexisting attractors and identify the mechanism for the creation of coexisting attractors. We find three types of routes to coexisting SNAs, including intermittent route, Heagy–Hammel route and fractalization route. The mechanisms for the creation of coexisting SNAs are investigated by the interruption of coexisting torus-doubling bifurcations. We characterize SNAs by the largest Lyapunov exponents, phase sensitivity exponents and power spectrum. Besides, the SNAs with extremely fractal basins exhibit sensitive dependence on the initial condition for some particular parameters.

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AN EXPERIMENTAL STUDY ON CHAOTIC DYNAMICS OF CFOA-BASED SC-CNN CIRCUIT

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127405013484 ◽

2005 ◽

Vol 15 (08) ◽

pp. 2551-2558 ◽

Cited By ~ 5

Author(s):

ENIS GÜNAY ◽

MUSTAFA ALÇI ◽

FATMA YILDIRIM

Keyword(s):

Neural Network ◽

High Frequency ◽

Chaotic Dynamics ◽

Laboratory Experiments ◽

Cellular Neural Network ◽

Current Feedback ◽

Op Amp ◽

Op Amps ◽

Experimental Implementation ◽

High Frequency Performance

In this paper, an experimental implementation of State Controlled Cellular Neural Network (SC-CNN) circuit using Current Feedback Op Amp (CFOA) is presented and its chaotic dynamics including high frequency performance are investigated by laboratory experiments. Depending on its significant advantages over the conventional voltage op amps (VOAs), without imposing any restrictions, the CFOAs have been used instead of the VOAs in SC-CNN circuit. Experimental results have shown that the proposed implementation has a capacity of higher frequency operation.

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STRANGE NONCHAOTIC ATTRACTORS IN A QUASIPERIODICALLY-FORCED PIECEWISE SMOOTH SYSTEM WITH FAREY TREE

Fractals ◽

10.1142/s0218348x19501184 ◽

2019 ◽

Vol 27 (07) ◽

pp. 1950118 ◽

Cited By ~ 3

Author(s):

YUNZHU SHEN ◽

YONGXIANG ZHANG

Keyword(s):

Lyapunov Exponents ◽

Scaling Laws ◽

Power Spectra ◽

Piecewise Smooth ◽

Largest Lyapunov Exponent ◽

Piecewise Smooth System ◽

Finite Time Lyapunov Exponents ◽

Farey Tree ◽

Strange Nonchaotic Attractors ◽

Smooth System

The existence of strange nonchaotic attractors (SNAs) is verified in a simple quasiperiodically-forced piecewise smooth system with Farey tree. It can be seen that more and more jumping discontinuities appear on the smooth torus and the torus becomes extremely fragmented with the change of control parameter. Finally, the torus becomes an SNA with fractal property. In order to confirm the existence of SNAs in this system, we preliminarily use the estimation of the phase sensitivity exponent, estimation of the largest Lyapunov exponent and rational approximation. SNAs are further characterized by power spectra, recurrence plots, the largest Lyapunov exponents and their variance, the distribution of the finite-time Lyapunov exponents, the spectral distribution function and scaling laws.

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HYPERCHAOS IN RTD-BASED CELLULAR NEURAL NETWORKS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127408022470 ◽

2008 ◽

Vol 18 (11) ◽

pp. 3439-3446 ◽

Cited By ~ 2

Author(s):

FENG-JUAN CHEN ◽

JI-BIN LI

Keyword(s):

Neural Network ◽

Neural Networks ◽

Lyapunov Exponents ◽

Cellular Neural Network ◽

Cellular Neural Networks ◽

Phase Portraits

In this paper, a hyperchaotic RTD-based cellular neural network is proposed and its hyperchaotic dynamics is demonstrated. The Lyapunov exponents spectrum is presented, and some typical Lyapunov exponents are calculated in a range of parameters. Several important phase portraits are presented as well.

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SC-CNN BASED MULTIFUNCTION SIGNAL GENERATOR

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127407020038 ◽

2007 ◽

Vol 17 (12) ◽

pp. 4387-4393 ◽

Cited By ~ 4

Author(s):

RECAI KILIÇ

Keyword(s):

Neural Network ◽

Computer Simulations ◽

Laboratory Experiments ◽

Cellular Neural Network ◽

Signal Generator ◽

Signal Generation ◽

Engineering Applications ◽

Chua's Circuit ◽

Future Studies ◽

Design Idea

This paper presents a very versatile multifunction signal generator tool. The proposed generator is based on State Controlled Cellular Neural Network (SC-CNN) based Chua's circuit and it has two signal generation modes, namely CM (Chaos Mode) and FM (Function Mode). While the generator is able to produce nonlinear chaotic waveforms in Chaos Mode, it is also able to generate other classical sinusoidal, triangle and square waveforms in Function Mode. The proposed design idea has been validated through computer simulations and laboratory experiments. Future studies with the proposed generator tool will contribute to further developments in SC-CNN based engineering applications.

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Strange Nonchaotic Attractors with Cellular Neural Networks

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127498001194 ◽

1998 ◽

Vol 08 (07) ◽

pp. 1551-1556 ◽

Cited By ~ 2

Author(s):

Zhiwen Zhu ◽

Shi Wang ◽

Henry Leung

Keyword(s):

Neural Network ◽

Dynamical System ◽

Poincaré Map ◽

Amplitude Spectrum ◽

Cellular Neural Network ◽

Poincare Map ◽

Fourier Amplitude ◽

Sinusoidal Input ◽

Strange Nonchaotic Attractors ◽

Fourier Amplitude Spectrum

In this paper, we investigate the existence of strange nonchaotic attractors in a nonautonomous cellular neural network (CNN). The network consists of two cells, each cell being driven by a sinusoidal input and the frequencies of two inputs being incommensurate. Numerical analyses based on Lyapunov exponent, Poincare map, double Poincare map, Fourier amplitude spectrum, and information dimension show the existence of strange nonchaotic attractors in a substantial parameter space. It appears that the CNN is the first dynamical system with separate excitations having the strange nonchaotic attractors.

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EXPERIMENTAL REALIZATION OF STRANGE NONCHAOTIC ATTRACTORS IN A NONLINEAR SERIES LCR CIRCUIT WITH NONSINUSOIDAL FORCE

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409025262 ◽

2009 ◽

Vol 19 (12) ◽

pp. 4131-4163 ◽

Cited By ~ 8

Author(s):

K. SRINIVASAN ◽

D. V. SENTHILKUMAR ◽

R. SURESH ◽

K. THAMILMARAN ◽

M. LAKSHMANAN

Keyword(s):

Lyapunov Exponents ◽

Electronic Circuit ◽

Numerical Data ◽

Electronic System ◽

Wave Force ◽

Distribution Functions ◽

Experimental Realization ◽

Square Wave ◽

Finite Time Lyapunov Exponents ◽

Strange Nonchaotic Attractors

We have identified several prominent routes, namely, fractalization, fractalization followed by intermittency, intermittency and Heagy–Hammel routes, for the birth of strange nonchaotic attractors (SNAs) in a quasiperiodically forced electronic system with nonsinusoidal (square wave) force as one of the quasiperiodic forces [Senthilkumar et al., 2008]. In addition, a new bubbling route has also been identified in this circuit. Although some of these prominent routes have been reported experimentally [Thamilmaran et al., 2006] in a quasiperiodically forced electronic circuit with both the forcings as sinusoidal forces, experimental identification of all these routes is reported here in a quasiperiodically forced electronic circuit with one of the forcings as a nonsinusoidal (square wave) force. The birth of SNAs by these routes are characterized from both the experimental and numerical data by the maximal Lyapunov exponents and their variance, Poincaré maps, Fourier amplitude spectra, spectral distribution functions and the distribution of finite-time Lyapunov exponents.

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