On a new hyperchaotic system

Qi, Guoyuan; Wyk, M.A. van; Wyk, Barend Jacobus van; Chen, Guanrong

doi:10.1016/j.physleta.2007.10.082

Cited by 97 publications

(57 citation statements)

References 32 publications

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“…This paper has examined control and synchronization of the new hyperchaotic systems performed by Qi et al [22] using the active backstepping control method. The proposed scheme is a systematic design approach and consists in a recursive procedure that interlaces the choice of a Lyapunov function with the design of active control.…”

Section: Discussionmentioning

confidence: 99%

“…The new 4D hyperchaotic system was performed by Qi et al [22]. This chaotic system, named as Qi system in this paper, is described by the following nonlinear differential equations.…”

Section: System Descriptionmentioning

confidence: 99%

“…[22]. The new hyperchaotic system has two large positive and one small negative Lyapunov exponents over the large range of parameters.…”

Section: Introductionmentioning

confidence: 96%

See 2 more Smart Citations

Control and Synchronization of New Hyperchaotic System using Active Backstepping Design

Yu¹,

Hyun²,

Park³

2011

International Journal of Fuzzy Logic and Intelligent Systems

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In this paper, an active backstepping design is proposed to achieve control and synchronization of a new hyperchaotic system. The proposed method is a systematic design approach and exists in a recursive procedure that interlaces the choice of a Lyapunov function with the design of the active control. The proposed controller enables stabilization of chaotic motion to the origin as well as synchronization of the two identical new hyperchaotic systems. Numerical simulations illustrate the validity of the proposed control technique.

show abstract

Section: Discussionmentioning

confidence: 99%

“…The new 4D hyperchaotic system was performed by Qi et al [22]. This chaotic system, named as Qi system in this paper, is described by the following nonlinear differential equations.…”

Section: System Descriptionmentioning

confidence: 99%

See 1 more Smart Citation

Control and Synchronization of New Hyperchaotic System using Active Backstepping Design

Yu¹,

Hyun²,

Park³

2011

International Journal of Fuzzy Logic and Intelligent Systems

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show abstract

“…[19] proposed two kinds of synchronization schemes for hyper chaotic systems using adaptive control. The hyper chaotic system they analyzed was presented by [27] and has two large positive and small negative Lyapunov exponents over a large range of parameters which makes it suitable for secure communications applications. [20] also investigated the synchronization of two hyper chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

A modified Chua chaotic oscillator and its application to secure communications

Zapateiro

Acho

Vidal

2014

Applied Mathematics and Computation

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In this paper, a new modified Chua oscillator is introduced. The original Chua oscillator is well known for its simple implementation and mathematical modeling. A modification of the oscillator is proposed in order to facilitate the synchronization and the encryption and decryption scheme. The modification consists in changing the nonlinear term of the original oscillator to a smooth and bounded nonlinear function. A bifurcation diagram, a Poincaré map and the Lyapunov exponents are presented as proofs of chaoticity of the newly modified oscillator. An application to secure communications is proposed in which two channels are used. Numerical simulations are performed in order to analyze the communication system.

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“…The study of chaos and hyperchaos are often emphasized on two main topics, one is to find practical schemes to stabilize hyperchaos (and chaos) and realize kinds of synchronization of hyperchaotic systems, another one is to construct new hyperchaotic or chaotic circuit in experiments [10,[17][18][19]. For example, Ma et al confirmed that chaotic neuron can be controlled to arbitrary periodical orbit by using phase compression scheme with one variable and the mechanism of this scheme is one kind of intermittent feedback scheme [20].…”

Section: Introductionmentioning

confidence: 99%

A time-varying hyperchaotic system and its realization in circuit

Zhang

et al. 2010

Nonlinear Dyn

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A hyperchaotic system is often used to generate secure keys or carrier wave for secure communication and the realistic hyperchaotic circuit often is made of capacitor, nonlinear resistor unit and induction coil. Parameters are often fixed in these hyperchaotic circuits and the hyperchaotic property of the system can be estimated by using a scheme of synchronization and time series analysis. In this paper, a time-varying hyperchaotic system is proposed by introducing changeable electric power source into the circuit; the changeable electric power source is combined with induction coil or capacitor in series to generate changeable output signals to excite the system. The diagrams of improved circuit are illustrated and critical parameters in experimental circuits are presented; the Lyapunov exponent spectrum vs. external applied electric power source is calculated. It is confirmed that the improved circuit always holds two positive Lyapunov exponents when the external electric power source works, and the chaotic attractors are much too different from the original one; thus, a more changeable hyperchaotic system is constructed in experiment.

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On a new hyperchaotic system

Cited by 97 publications

References 32 publications

Control and Synchronization of New Hyperchaotic System using Active Backstepping Design

Control and Synchronization of New Hyperchaotic System using Active Backstepping Design

A modified Chua chaotic oscillator and its application to secure communications

A time-varying hyperchaotic system and its realization in circuit

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