A novel four-wing non-equilibrium chaotic system and its circuit implementation

Lin, Yandan; Wang, Chunhua; He, Haizhen; Zhou, Lili

doi:10.1007/s12043-015-1118-1

Cited by 36 publications

(7 citation statements)

References 20 publications

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“…There are kinds of methods to measure the complexity, such as spectrum entropy (SE), C 0 entropy, and permutation entropy (PE) [ 40 , 41 , 42 ]. Among them, PE algorithm is a proper choice to estimate the numerical series accurately and rapidly.…”

Section: Dynamics Analysis Of the Complex Chaotic Systemsmentioning

confidence: 99%

Complex Chaotic Attractor via Fractal Transformation

Dai

Sun

et al. 2019

Entropy

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Based on simplified Lorenz multiwing and Chua multiscroll chaotic systems, a rotation compound chaotic system is presented via transformation. Based on a binary fractal algorithm, a new ternary fractal algorithm is proposed. In the ternary fractal algorithm, the number of input sequences is extended from 2 to 3, which means the chaotic attractor with fractal transformation can be presented in the three-dimensional space. Taking Lorenz system, rotation Lorenz system and compound chaotic system as the seed chaotic systems, the dynamics of the complex chaotic attractors with fractal transformation are analyzed by means of bifurcation diagram, complexity and power spectrum, and the results show that the chaotic sequences with fractal transformation have higher complexity. As the experimental verification, one kind of complex chaotic attractors is implemented by DSP, and the result is consistent with that of the simulation, which verifies the feasibility of digital circuit implement.

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Section: Dynamics Analysis Of the Complex Chaotic Systemsmentioning

confidence: 99%

Complex Chaotic Attractor via Fractal Transformation

Dai

Sun

et al. 2019

Entropy

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“…Through the above method, Miranda and Stone (1993) first proposed the generation of multi-wing attractor in Lorenz system in 1993. After that, a large number of four-wing chaotic systems have been reported (Lin et al, 2016;Signing et al, 2018;Xie et al, 2017). Especially in the past decade, a class of four-wing chaotic systems with more complex dynamic behaviors were proposed.…”

Section: Introductionmentioning

confidence: 99%

One-to-four-wing hyperchaotic fractional-order system and its circuit realization

Wen

2020

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Purpose This paper aims to introduce a novel 4D hyperchaotic fractional-order system which can produce one-to-four-wing hyperchaotic attractors. In the study of chaotic systems with variable-wing attractors, although some chaotic systems can generate one-to-four-wing attractors, none of them are hyperchaotic attractors, which is incomplete for the dynamic characteristics of chaotic systems. Design/methodology/approach A novel 4D fractional-order hyperchaotic system is proposed based on the classical three-dimensional Lü system. The complex and abundant dynamic behaviors of the fractional-order system are analyzed by phase diagrams, bifurcation diagrams and the corresponding Lyapunov exponents. In addition, SE and C0 algorithms are used to analyze the complexity of the fractional-order system. Then, the influence of order q on the system is also investigated. Finally, the circuit is implemented using physical components. Findings The most particular interest is that the system can generate one-to-four-wing hyperchaotic attractors with only one parameter variation. Then, the hardware circuit experimental results tally with the numerical simulations, which proves the validity and feasibility of the fractional-order hyperchaotic system. Besides, under different initial conditions, coexisting attractors can be obtained by changing the parameter d or the order q. Then, the complexity analysis of the system shows that the fractional-order chaotic system has higher complexity than the corresponding integer-order chaotic system. Originality/value The circuit structure of the fractional-order hyperchaotic system is simple and easy to implement, and one-to-four-wing hyperchaotic attractors can be observed in the circuit. To the best of the knowledge, this unique phenomenon has not been reported in any literature. It is of great reference value to analysis and circuit realization of fractional-order chaotic systems.

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“…Attractors with no equilibrium or with only one stable equilibrium are considered as "hidden", because their basins of attraction do not intersect with small neighborhoods of the equilibria. Due to their "hidden" feature, which is difficult to be found in systems, researchers have extensively explored chaotic attractors with no equilibria [Wei, 2011;Pham et al, 2014;Lin et al, 2016;Pham et al, 2016a;Wang et al, 2016;Yu et al, 2016;Dantsev, 2018;Zhan et al, 2018] and with only one stable equilibrium [Wei & Yang, 2011;Wang & Chen, 2012;Molate et al, 2013;Wei & Zhang, 2014]. Some elementary quadratic chaotic flows with no equilibria were studied firstly [Wei, 2011;Pham et al, 2014;Dantsev, 2018].…”

Section: Introductionmentioning

confidence: 99%

“…Some elementary quadratic chaotic flows with no equilibria were studied firstly [Wei, 2011;Pham et al, 2014;Dantsev, 2018]. Then some hyper-chaotic attractors with no equilibria were investigated Pham et al, 2016a] and multi-wing non-equilibrium attractors were considered [Yu et al, 2016;Wang et al, 2016;Lin et al, 2016;Zhan et al, 2018]. Furthermore, some chaotic flows with one stable equilibrium [Wei & Yang, 2011;Wang & Chen, 2012;Molate et al, 2013] and hyper-chaotic flows with one stable equilibrium [Wei & Zhang, 2014] were investigated.…”

Section: Introductionmentioning

confidence: 99%

A New Class of Two-Dimensional Chaotic Maps with Closed Curve Fixed Points

Jiang

Liu

Wei

et al. 2019

Int. J. Bifurcation Chaos

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This paper constructs a new class of two-dimensional maps with closed curve fixed points. Firstly, the mathematical model of these maps is formulated by introducing a nonlinear function. Different types of fixed points which form a closed curve are shown by choosing proper parameters of the nonlinear function. The stabilities of these fixed points are studied to show that these fixed points are all nonhyperbolic. Then a computer search program is employed to explore the chaotic attractors in these maps, and several simple maps whose fixed points form different shapes of closed curves are presented. Complex dynamical behaviors of these maps are investigated by using the phase-basin portrait, Lyapunov exponents, and bifurcation diagrams.

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A novel four-wing non-equilibrium chaotic system and its circuit implementation

Cited by 36 publications

References 20 publications

Complex Chaotic Attractor via Fractal Transformation

Complex Chaotic Attractor via Fractal Transformation

One-to-four-wing hyperchaotic fractional-order system and its circuit realization

A New Class of Two-Dimensional Chaotic Maps with Closed Curve Fixed Points

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