Generating tri-chaos attractors with three positive Lyapunov exponents in new four order system via linear coupling

Li, Shih Yu; Huang, Sheng‐Chieh; Yang, Cheng Hsiung; Ge, Zheng Ming

doi:10.1007/s11071-011-0306-x

Cited by 21 publications

(10 citation statements)

References 40 publications

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“…Nonlinear dynamics, commonly called the chaos theory, changes the scientific way of looking at the dynamics of natural and social systems, which has been intensively studied over the past several decades [1][2][3][4][5][6][7][8][9][10]. The phenomenon of chaos has attracted widespread attention amongst mathematicians, physicists, and engineers and has also been extensively studied in many fields, such as chemical reactions [11,12], biological systems [13,14], information processing [15,16], and secure communications [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Chaotic Motions in the Real Fuzzy Electronic Circuits

Yang

Lin

et al. 2013

Abstract and Applied Analysis

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Fuzzy electronic circuit (FEC) is firstly introduced, which is implementing Takagi-Sugeno (T-S) fuzzy chaotic systems on electronic circuit. In the research field of secure communications, the original source should be blended with other complex signals. Chaotic signals are one of the good sources to be applied to encrypt high confidential signals, because of its high complexity, sensitiveness of initial conditions, and unpredictability. Consequently, generating chaotic signals on electronic circuit to produce real electrical signals applied to secure communications is an exceedingly important issue. However, nonlinear systems are always composed of many complex equations and are hard to realize on electronic circuits. Takagi-Sugeno (T-S) fuzzy model is a powerful tool, which is described by fuzzy IF-THEN rules to express the local dynamics of each fuzzy rule by a linear system model. Accordingly, in this paper, we produce the chaotic signals via electronic circuits through T-S fuzzy model and the numerical simulation results provided by MATLAB are also proposed for comparison. T-S fuzzy chaotic Lorenz and Chen-Lee systems are used for examples and are given to demonstrate the effectiveness of the proposed electronic circuit.

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Section: Introductionmentioning

confidence: 99%

Chaotic Motions in the Real Fuzzy Electronic Circuits

Yang

Lin

et al. 2013

Abstract and Applied Analysis

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“…In fact, a hyperchaotic system has more than one positive Lyapunov exponent and consequently its dynamics can be expanded more than one direction [2][3][4]. Because of the presence of more than one positive exponent, it exhibits more complex dynamical behaviors, increased randomness and higher unpredictability compared with a chaotic system [5,6].…”

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confidence: 99%

“…A diversity of applications has been introduced for hyperchaotic systems in different fields including nonlinear circuits, laser, cryptography and secure communications due to their mentioned distinguished properties. Motivated by the above discussion, introducing and generating new hyperchaotic systems has become an interesting topic among researches [2,3,[5][6][7][8][9][10][11][12][13][14][15][16]. No clear and systematic method has been suggested to create a hyperchaotic system so far.…”

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confidence: 99%

“…In the first method, a new state variable is added to a three-dimensional autonomous chaotic system. In fact, this method extends the dimension of low dimensional chaotic system because the minimum dimension of an autonomous dynamical system should be at least four to show hyperchaos phenomenon [2][3][4][5][6][7][8][9][10][11][12]. In reference [2], a nonlinear state feedback control has been applied to generate hyperchaos phenomenon from the Chua chaotic system with smooth cubic nonlinearity.…”

mentioning

confidence: 99%

“…In reference [2], a nonlinear state feedback control has been applied to generate hyperchaos phenomenon from the Chua chaotic system with smooth cubic nonlinearity. Reference [3] has coupled Mathieu and Van der Pol systems via linear feedback control to present a new hyperchaotic system with three Lyapunov exponents. References [4][5][6] have proposed four new hyperchaotic systems by adding linear controllers to the Qi and Rabinovich systems.…”

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confidence: 99%

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Introducing and circuit implementation of a novel non-autonomous hyperchaotic system based on Qi chaotic system

Abooee

Jahed‐Motlagh

2014

2014 22nd Iranian Conference on Electrical Engineering (ICEE)

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In this paper a new hyperchaotic system is proposed by sinusoidal perturbation of the three-dimensional Qi chaotic system. The sinusoidal perturbation term is added to one of the constant parameters of Qi chaotic system. Then, hyperchaos phenomenon is appeared in the mentioned system by changing amplitude and frequency of the sinusoidal perturbation term. To show the introduced system has hyperchaotic behaviors, its Lyapunov exponents are calculated with respect to amplitude and frequency of sinusoidal perturbation term. Computer based numerical simulation results illustrate that hyperchaos phenomenon can be observed in the presented system by proper selections of the values of amplitude and frequency of sinusoidal perturbation term. More, an electronic circuit is designed to realize the differential equations of new hyperchaotic system. The designed electronic circuit is implemented and tested by Orcad-PSpice software. Experimental observations by using Orcad-PSpice software verify the numerical simulation results properly.

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