A novel bounded 4D chaotic system

Zhang, Jianxiong

doi:10.1007/s11071-011-0159-3

Cited by 31 publications

(12 citation statements)

References 22 publications

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“…China e-mail: liuyongjianmaths@126.com simple nonlinearities [3][4][5][6][7][8][9][10][11][12][13]. It is very important to note that some 3D autonomous chaotic systems have three particular fixed points: one saddle and two unstable saddle-foci (for example, the Lorenz system [1], the Chen system [3], the Lü system [4], and the conjugate Lorenz-type system [14]).…”

Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

Analysis of global dynamics in an unusual 3D chaotic system

Liu

2012

Nonlinear Dyn

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In order to further understand a complex three-dimensional (3D) dynamical system showing strange chaotic attractors with two stable node-foci as its only equilibria, we analyze dynamics at infinity of the system. First, we give the complete description of the phase portrait of the system at infinity, and perform a numerical study on how the solutions reach the infinity, depending on the parameter values. Then, combining analytical and numerical techniques, we find that for the parameter value b = 0, the system presents an infinite set of singularly degenerate heteroclinic cycles. It is hoped that these global study can give a contribution in understanding of this unusual chaotic system, and will shed some light leading to final revealing the true geometrical structure and the essence of chaos for the chaotic attractor.

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Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

Analysis of global dynamics in an unusual 3D chaotic system

Liu

2012

Nonlinear Dyn

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“…By now, the usual technique to get a new hyper-chaotic system is to add one more state variable to the three-dimensional chaotic systems, just as the Lorenz system [1], Chen system [21], Lü system [22], Qi system [23] and so on. There also some hyperchaotic system is constructed directly [17,38,39], but this is difficult.…”

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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“…By now, the usual technique to get a new 4D smooth quadratic autonomous hyper-chaotic system [4][5][6][7][8][9][10] is to add one more state variable to the three dimensional chaotic system, just as the Lorenz system [11], Chen system [12], Lü system [13], Qi system [14] and so on. There also some hyper-chaotic system is constructed directly [15][16][17][18], but this is difficult.…”

Section: Introductionmentioning

confidence: 99%

“…It is a challenge work to estimate the ultimate boundary region of a chaotic attractor. One usual way is through the optimization technique and Lyapunov function to achieve the ultimate boundary regions of some existing chaotic systems [18,[22][23][24][25][26]. Recently, also utilizing the Lyapunov function, stability theory and the optimization technique, a unified approach was constructed by Wang et al [27] to estimate the ultimate boundary regions of a class of high dimensional quadratic autonomous dynamical system (HDQADS).…”

Section: Introductionmentioning

confidence: 99%

Local bifurcation analysis and ultimate bound of a novel 4D hyper-chaotic system

et al. 2014

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This paper presents a new four-dimensional smooth quadratic autonomous hyper-chaotic system which can generate novel two double-wing periodic, quasi-periodic and hyper-chaotic attractors. The Lyapunov exponent spectrum, bifurcation diagram and phase portrait are provided. It is shown that this system has a wide hyper-chaotic parameter. The pitchfork bifurcation and Hopf bifurcation are discussed using the center manifold theory. The ellipsoidal ultimate bound of the typical hyper-chaotic attractor is observed. Numerical simulations are given to demonstrate the evolution of the two bifurcations and show the ultimate boundary region.

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A novel bounded 4D chaotic system

Cited by 31 publications

References 22 publications

Analysis of global dynamics in an unusual 3D chaotic system

Analysis of global dynamics in an unusual 3D chaotic system

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

Local bifurcation analysis and ultimate bound of a novel 4D hyper-chaotic system

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