Multi-wing hyperchaotic attractors from coupled Lorenz systems

Grassi, Giuseppe; Severance, Frank L.; Miller, D.A.

doi:10.1016/j.chaos.2007.12.003

Cited by 60 publications

(22 citation statements)

References 26 publications

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“…The Cang's system is hyperchaotic and fourwinged, but it has five equilibrium points. Normally, a four-wing hyperchaotic attractor can be generated from a nonlinear system of more than four differential equations [43]. So far, in literature, there is no reported 3D or 4D smooth autonomous system with only one equilibrium that can generate a four-wing and hyperchaotic attractor.…”

Section: Introductionmentioning

confidence: 99%

Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form

Dadras

Momeni

et al. 2011

Nonlinear Dyn

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In this paper, a new simple 4D smooth autonomous system is proposed, which illustrates two interesting rare phenomena: first, this system can generate a four-wing hyperchaotic and a four-wing chaotic attractor and second, this generation occurs under condition that the system has only one equilibrium point at the origin. The dynamic analysis approach in the paper involves time series, phase portraits, Lyapunov exponents, bifurcation diagram, and Poincaré maps, to investigate some basic dynamical behaviors of the proposed 4D system. The physical existence of the fourwing hyperchaotic attractor is verified by an electronic circuit. Finally, it is shown that the fractional-order S. Dadras · H.R. Momeni ( ) Automation and Instruments Lab, form of the system can also generate a chaotic fourwing attractor.

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Section: Introductionmentioning

confidence: 99%

Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form

Dadras

Momeni

et al. 2011

Nonlinear Dyn

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“…Hyperchaos was firstly reported by Rossler in 1979 [24]. Since then, many hyperchaotic systems have been proposed by employing state feedback control [3,8,22], parameter perturbation [15,26], or coupling approach [11,20].…”

Section: Introductionmentioning

confidence: 99%

Scaling Synchronization of a 6D Hyperchaotic System

Osman¹,

Zhu²,

Yang³

2018

dtcse

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Abstract. This paper focuses on the scaling synchronization issue of a 6D hyperchaotic system with one or three equilibria which is obtained by controlling a 5D hyperchaotic system that is formed by adding a linear feedback controller and a nonlinear feedback controller to the Lorenz system. When the parameters are known in advance, applying the one-way linear coupling approach to synchronize the 6D hyperchaotic system up to a scaling factor. When the parameters are fully unknown, utilizing the adaptive method to synchronize the uncertain 6D hyperchaotic system up to a scaling factor. Finally, many numerical simulations have been carried out to verify the validation and efficiency of the proposed schemes.

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“…Similarly, the generations of autonomous chaotic systems with multi-scroll or multi-wing attractor [13][14][15] were sometimes considered a key issue for many engineering applications. Thus, creating a memristive system with a multi-scroll or multi-wing attractor has a practical significance, which is the motivation of this paper.…”

Section: Introductionmentioning

confidence: 99%

“…At first, it was believed that this system could produce a four-wing chaotic attractor, but later it had been proved that the four-wing chaotic attractor of this system could not actually exist in theory [13]. By adding a memristor and a crossproduct item into this 3-D chaotic system, a 4-D memristive system can be obtained.…”

Section: Introductionmentioning

confidence: 99%

A four-wing hyper-chaotic attractor generated from a 4-D memristive system with a line equilibrium

et al. 2015

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A new hyper-chaotic system is presented in this paper by adding a smooth flux-controlled memristor and a cross-product item into a three-dimensional autonomous chaotic system. It is exciting that this new memristive system can show a four-wing hyperchaotic attractor with a line equilibrium. The dynamical behaviors of the proposed system are analyzed by Lyapunov exponents, bifurcation diagram and Poincaré maps. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of hyperchaos in the system is verified theoretically. Finally, an electronic circuit is designed to implement the hyperchaotic memristive system.

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Multi-wing hyperchaotic attractors from coupled Lorenz systems

Cited by 60 publications

References 26 publications

Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form

Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form

Scaling Synchronization of a 6D Hyperchaotic System

A four-wing hyper-chaotic attractor generated from a 4-D memristive system with a line equilibrium

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