A hyperchaotic system without equilibrium

Wang, Zenghui; Cang, Shijian; Ochola, Elisha Oketch; Sun, Yanxia

doi:10.1007/s11071-011-0284-z

Cited by 143 publications

(58 citation statements)

References 14 publications

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“…A System without Equilibrium. Chaotic systems without equilibrium attract have been attracting a lot of interest [38][39][40][41][42]. When mentioning a chaotic system without equilibrium, it means that there is no real equilibrium in such a system.…”

Section: A System Without Equilibrium Andmentioning

confidence: 99%

Multimedia Security Application of a Ten-Term Chaotic System without Equilibrium

et al. 2017

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A system without equilibrium has been proposed in this work. Although there is an absence of equilibrium points, the system displays chaos, which has been confirmed by phase portraits and Lyapunov exponents. The system is realized on an electronic card, which exhibits chaotic signals. Furthermore, chaotic property of the system is applied in multimedia security such as image encryption and sound steganography.

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Section: A System Without Equilibrium Andmentioning

confidence: 99%

Multimedia Security Application of a Ten-Term Chaotic System without Equilibrium

et al. 2017

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“…It is interesting that Wang et al found a hyperchaotic system without equilibrium [13], which is different from normal hyperchaotic systems. Following up the first discovery of Wang et al, other hyperchaotic systems without equilibrium were presented [14][15][16][17].…”

Section: Introductionmentioning

confidence: 98%

A No-Equilibrium Hyperchaotic System and Its Fractional-Order Form

Hoàng

Kingni

Pham

2017

Mathematical Problems in Engineering

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No-equilibrium system with chaotic behavior has attracted considerable attention recently because of its hidden attractor. We study a new four-dimensional system without equilibrium in this work. The new no-equilibrium system exhibits hyperchaos and coexisting attractors. Amplitude control feature of the system is also discovered. The commensurate fractional-order version of the proposed system is studied using numerical simulations. By tuning the commensurate fractional-order, the proposed system displays a wide variety of dynamical behaviors ranging from coexistence of quasiperiodic and chaotic attractors and bistable chaotic attractors to point attractor via transient chaos.

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“…Surprisingly, chaotic attractors can also be hidden in the case of the deterministic dynamical systems without equilibrium as shown in Refs. [34][35][36][37][38][39][40]. Even more interesting discoveries are chaotic systems having only a stable¯xed point; for further study, consult Refs.…”

Section: Introductionmentioning

confidence: 99%

Current-Mode Network Structures Dedicated for Simulation of Dynamical Systems with Plane Continuum of Equilibrium

Petržela

Götthans

Guzan

2018

J CIRCUIT SYST COMP

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This review paper describes di®erent lumped circuitry realizations of the chaotic dynamical systems having equilibrium degeneration into a plane object with topological dimension of the equilibrium structure equals one. This property has limited amount (but still increasing, especially recently) of third-order autonomous deterministic dynamical systems. Mathematical models are generalized into classes to design analog networks as universal as possible, capable of modeling the rich scale of associated dynamics including the so-called chaos. Reference state trajectories for the chaotic attractors are generated via numerical analysis. Since used active devices can be precisely approximated by using third-level frequency dependent model, it is believed that computer simulations are close enough to capture real behavior. These simulations are included to demonstrate the existence of chaotic motion.

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A hyperchaotic system without equilibrium

Cited by 143 publications

References 14 publications

Multimedia Security Application of a Ten-Term Chaotic System without Equilibrium

Multimedia Security Application of a Ten-Term Chaotic System without Equilibrium

A No-Equilibrium Hyperchaotic System and Its Fractional-Order Form

Current-Mode Network Structures Dedicated for Simulation of Dynamical Systems with Plane Continuum of Equilibrium

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