A new type of four-wing chaotic attractors in 3-D quadratic autonomous systems

Wang, Zenghui; Qi, Guoyuan; Sun, Yanxia; Wyk, Barend Jacobus van; Wyk, M.A. van

doi:10.1007/s11071-009-9607-8

Cited by 30 publications

(19 citation statements)

References 29 publications

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“…On account of its complicated topological structure, generating multi-wing chaotic attractors from these smooth systems becomes a very important research topic. Some papers in recent years have presented many practical and suitable methods to create multi-scroll or multi-wing attractors, and these methods are as follows: piecewise linear (PWL) function method, sine function, stair function, some nonlinear functions including switching, hysteresis and saturated functions [42,45].…”

Section: Introductionmentioning

confidence: 99%

Complex dynamics in a 5-D hyper-chaotic attractor with four-wing, one equilibrium and multiple chaotic attractors

Zarei

2015

Nonlinear Dyn

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In this paper, a new five-dimensional autonomous hyper-chaotic attractor with complex dynamics is introduced. Nonlinear behavior of the proposed system is different with most well-known chaotic and hyper-chaotic attractors and exists interesting aspects in this system. There are eight parameters to control with only one equilibrium point, and the new dynamics can generate four-wing hyperchaotic and chaotic attractors for some specific parameters and initial conditions. One remarkable feature of the new system is that it can generate double-wing and four-wing smooth chaotic attractors with special appearance. By using the symmetry properties about the coordinates, initial conditions and bifurcation diagrams, many schemes are presented to indicate multiscroll or multi-wing systems. The phenomenon of multiple attractors is discussed, which means that several attractors created simultaneously from different initial values, and according to this phenomenon, many strange attractors are obtained. Detailed information on the dynamic of the new system is obtained numerically by means of phase portraits, sensitivity to initial conditions, Lyapunov exponents spectrum, bifurcation diagrams and Poincare maps. The stability analysis of the new attractors has been investigated to understand dynamical behaviors nearby equilibrium points.

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Section: Introductionmentioning

confidence: 99%

Complex dynamics in a 5-D hyper-chaotic attractor with four-wing, one equilibrium and multiple chaotic attractors

Zarei

2015

Nonlinear Dyn

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“…It is expected that those chaotic systems will have a certain theoretical and practical significance for secure communication, control processing, and some other engineering applications. There exist some well-known fractional-order systems and multi-wing systems, such as the fractional-order Chua's circuit [7], the fractional-order Rössler system [8], the fractional-order Chen system [9],the fractional-order Lu system [10], the first true four-wing attractor [11], a family of hyperchaotic systems with four-wing attractor [12], among many others [13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Inverse Optimal Control of a Novel Fractional-Order Four-Wing Hyperchaotic System with Uncertain Parameter and Circuitry Implementation

Yang

2015

Mathematical Problems in Engineering

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An efficient approach of inverse optimal control and adaptive control is developed for global asymptotic stabilization of a novel fractional-order four-wing hyperchaotic system with uncertain parameter. Based on the inverse optimal control methodology and fractional-order stability theory, a control Lyapunov function (CLF) is constructed and an adaptive state feedback controller is designed to achieve inverse optimal control of a novel fractional-order hyperchaotic system with four-wing attractor. Then, an electronic oscillation circuit is designed to implement the dynamical behaviors of the fractional-order four-wing hyperchaotic system and verify the satisfactory performance of the controller. Comparing with other fractional-order chaos control methods which may have more than one nonlinear state feedback controller, the inverse optimal controller has the advantages of simple structure, high reliability, and less control effort that is required and can be implemented by electronic oscillation circuit.

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“…In 1976, Rossler conducted important work that rekindled the interest in three-dimensional (3D) dissipative dynamical systems [5]. Then, many Lorenz-like or Lorenzbased chaotic systems were proposed and investigated [6][7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Generation of a New Three Dimension Autonomous Chaotic Attractor and its Four Wing Type

Wang

2013

Eng. Technol. Appl. Sci. Res.

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In this paper, a new three-dimension (3D) autonomous chaotic system with a nonlinear term in the form of a hyperbolic sine (or cosine) function is reported. Some interesting and complex attractors are obtained. Basic dynamical properties of the new chaotic system are demonstrated in terms of Lyapunov exponents, Poincare mapping, fractal dimension and continuous spectrum. Meanwhile, for further enhancing the complexity of the topological structure of the new chaotic attractors, the attractors are changed from two-wing to four-wing through making axis doubly polarized, theoretically analyzed and numerically simulated. The obtained results clearly show that the chaotic system deserves further detailed investigation.

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A new type of four-wing chaotic attractors in 3-D quadratic autonomous systems

Cited by 30 publications

References 29 publications

Complex dynamics in a 5-D hyper-chaotic attractor with four-wing, one equilibrium and multiple chaotic attractors

Complex dynamics in a 5-D hyper-chaotic attractor with four-wing, one equilibrium and multiple chaotic attractors

Adaptive Inverse Optimal Control of a Novel Fractional-Order Four-Wing Hyperchaotic System with Uncertain Parameter and Circuitry Implementation

Generation of a New Three Dimension Autonomous Chaotic Attractor and its Four Wing Type

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