A necessary condition for double scroll attractor existence in fractional-order systems

Tavazoei, Mohammad Saleh; Haeri, ءMohammad

doi:10.1016/j.physleta.2007.05.081

Cited by 332 publications

(152 citation statements)

References 25 publications

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“…Fractional-order system (2) has five equilibrium points. They are 0 = (0, 0, 0), Tavazoei and Haeri [17] have obtained that a necessary condition for a fractional-order nonlinear system to exist chaotic is…”

Section: System Model and Basic Characteristicsmentioning

confidence: 99%

A Fractional‐Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller

Zhou

Pan

2018

Complexity

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A 3D fractional-order nonlinear system with coexisting chaotic attractors is proposed in this paper. The necessary condition of the existence chaos is ≥ 0.8477. The fractional-order system exhibits chaotic attractors with the order as low as 2.5431. The largest Lyapunov exponent varying as fractional order is given. Furthermore, there are the coexisting "positive attractor" and "negative attractor" in this fractional-order chaotic system, and the necessary condition for "positive attractor" and "negative attractor" is obtained. Meanwhile, a control scheme for the stabilization of the unstable equilibrium is suggested via a single state variable linear controller. Numerical results show that the control scheme is valid.

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Section: System Model and Basic Characteristicsmentioning

confidence: 99%

A Fractional‐Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller

Zhou

Pan

2018

Complexity

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“…Time histories of system (11) for y signal at the equilibrium E 0 with α = 0.9: (a) t max = 100, (b) t max = 300.…”

Section: Active Control Of the Fractional Order Chaotic Systemmentioning

confidence: 99%

“…It has been shown that nonlinear chaotic systems may keep their chaotic behavior when their models become fractional [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Active Control of a Chaotic Fractional Order Economic System

Baskonus

Mekkaoui²,

Hammouch³

et al. 2015

Entropy

142

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“…Clearly, the points E 1 E 2 are saddle points of index two and E 3 is a saddle point of index one. It is discussed by Tavazoei and Haeri in [36] that the chaotic scrolls are generated only around the saddle points of index two and the saddle points of index one are responsible only for connecting these scrolls.…”

Section: Fractional Yu-wang Systemmentioning

confidence: 99%

Dynamics analysis of fractional order Yu-Wang system

Bhalekar

2013

Open Physics

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Abstract:Fractional order version of a dynamical system introduced by Yu and Wang (Engineering, Technology & Applied Science Research, 2, (2012) 209-215) is discussed in this article. The basic dynamical properties of the system are studied. Minimum effective dimension 0.942329 for the existence of chaos in the proposed system is obtained using the analytical result. For chaos detection, we have calculated maximum Lyapunov exponents for various values of fractional order. Feedback control method is then used to control chaos in the system. Further, the system is synchronized with itself and with fractional order financial system using active control technique. Modified Adams-Bashforth-Moulton algorithm is used for numerical simulations. PACS

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A necessary condition for double scroll attractor existence in fractional-order systems

Cited by 332 publications

References 25 publications

A Fractional‐Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller

A Fractional‐Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller

Active Control of a Chaotic Fractional Order Economic System

Dynamics analysis of fractional order Yu-Wang system

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