Chaos control of fractional order Rabinovich–Fabrikant system and synchronization between chaotic and chaos controlled fractional order Rabinovich–Fabrikant system

Srivastava, Mayank; Agrawal, Saurabh; Vishal, K.; Das, S.

doi:10.1016/j.apm.2013.11.054

Cited by 35 publications

(16 citation statements)

References 22 publications

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“…where l is a positive constant and 0  is the initial value of the update vector parameter  . Using equation 17and 18, we design the following controller; ( , , ) g y y y  , together with the external turbulences 1 () dt and 2 () dt are practically unknown functions, they must be known to apply the control law (20). To overcome this problem, the control law (20) is assumed to be rewritten with the help of assumption 3.2 as follows: 1 2 3 1 2 3 2 2 1 1 1 2 3 2 3 1 2 3 2 1 1 1 2 3 2 3 1 2 3 2 2…”

Section: Design Of Switching Surfacementioning

confidence: 99%

“…With the comparative rule application of (19) and (20), and the controller (21) 1 2 3 2 1 2 3 2 1 2 3 1 2 3 2 2 1 1 1 2 3 2 3 1 2 3 2 1 1 1 2 3 2 3 1 2 3 2 2 2 1 1 1 2…”

Section: Design Of Switching Surfacementioning

confidence: 99%

“…Examples include investigations into the chaotic behavior of fractional -order horizontal platform systems [19] and many published articles on fractional -order chaotic systems [20][21][22][23]. Among the hottest topics that have been investigated and explored widely in the field of nonlinear science are synchronization and control of chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Synchronization of a Novel Class of Fractional-Order Uncertain Chaotic Systems via Adaptive Sliding Mode Controller

Riahi¹,

Noghredani²,

Shajiee³

et al. 2016

IJCA

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In this work an adaptive sliding mode controller in the presence of uncertainty, as well as the external disturbance is considered. A concise introduction and investigation of the dynamic behavior of a novel class of chaotic systems with fractional order derivatives for synchronization is presented. It is supposed that the high bounds of uncertainty and external disturbance are unknown. The proposed controller is designed based on error dynamics and acceptable adaptive laws. The sliding mode dynamic stability and the condition to start sliding are proved by Lyapunov stability theory. With this new proposed approach, Chen and Lorenz system with fractional order derivatives are synchronized. Finally, simulation results with MATLAB software showed that the designed comparative sliding mode controller was able to synchronize chaotic systems with fractional order derivatives in the presence of the mentioned adverse factors. The main characteristic of the proposed method compared to other methods is providing acceptable adaptive laws for satisfactory functioning against uncertainty and external disturbance and eliminate the chattering phenomenon for synchronization of non-identical chaotic systems with fractional order derivatives.

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Section: Design Of Switching Surfacementioning

confidence: 99%

“…With the comparative rule application of (19) and (20), and the controller (21) 1 2 3 2 1 2 3 2 1 2 3 1 2 3 2 2 1 1 1 2 3 2 3 1 2 3 2 1 1 1 2 3 2 3 1 2 3 2 2 2 1 1 1 2…”

Section: Design Of Switching Surfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Synchronization of a Novel Class of Fractional-Order Uncertain Chaotic Systems via Adaptive Sliding Mode Controller

Riahi¹,

Noghredani²,

Shajiee³

et al. 2016

IJCA

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show abstract

“…In fact, the interest in this system is continuously increasing (see e.g. [3,4,5,6,7,8,9,10]). The mathematical RF model is defined by the following system of ODEs:…”

Section: Introductionmentioning

confidence: 99%

Unusual dynamics and hidden attractors of the Rabinovich–Fabrikant system

2016

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“…Compared with the numerical investigation reported in [Rabinovich & Fabrikant(1979)], the studies in [Danca & Chen(2004)] (and also in [Luo et al(2007)]), revealed some new interesting aspects. Since then, the interest in this system, has continuously increased, partially following the direction of [Danca & Chen(2004)] (see [Chairez(2014), Azzaz et al(2013), Serrano-Guerrero et al(2013), Motsa et al(2012), Zhang et al(2011), Srivastava et al(2014), Umoh & Edwin(2013), Agrawal et al(2012)], utilizing some computer software such as Matlab Central [Moysis(2014)] or Wolfram [Craven(1011)]).…”

mentioning

confidence: 99%

Looking More Closely at the Rabinovich–Fabrikant System

Danca

Fečkan

Kuznetsov

et al. 2016

Int. J. Bifurcation Chaos

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Recently, we look more closely into the Rabinovich-Fabrikant system, after a decade of the study in [Danca & Chen(2004)], discovering some new characteristics such as cycling chaos, transient chaos, chaotic hidden attractors and a new kind of saddles-like attractor. In addition to extensive and accurate numerical analysis, on the assumptive existence of heteroclinic orbits, we provide a few of their approximations.

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Chaos control of fractional order Rabinovich–Fabrikant system and synchronization between chaotic and chaos controlled fractional order Rabinovich–Fabrikant system

Cited by 35 publications

References 22 publications

Synchronization of a Novel Class of Fractional-Order Uncertain Chaotic Systems via Adaptive Sliding Mode Controller

Synchronization of a Novel Class of Fractional-Order Uncertain Chaotic Systems via Adaptive Sliding Mode Controller

Unusual dynamics and hidden attractors of the Rabinovich–Fabrikant system

Looking More Closely at the Rabinovich–Fabrikant System

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