Chaotic attractors in incommensurate fractional order systems

Tavazoei, Mohammad Saleh; Haeri, ءMohammad

doi:10.1016/j.physd.2008.03.037

Cited by 317 publications

(168 citation statements)

References 38 publications

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“…In order to numerically examine and avoid the linear dependence of the related functions [12,26], we let α 1 = 0.6, α 2 = 0.8, α 3 = 0.99. All of the other settings remain unchanged as stated in Section 4.1.…”

Section: The Impact Of Fractional Order On the Identification Processmentioning

confidence: 99%

Adaptive Synchronization of Fractional Neural Networks with Unknown Parameters and Time Delays

et al. 2014

Entropy

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In this paper, the parameters identification and synchronization problem of fractional-order neural networks with time delays are investigated. Based on some analytical techniques and an adaptive control method, a simple adaptive synchronization controller and parameter update laws are designed to synchronize two uncertain complex networks with time delays. Besides, the system parameters in the uncertain network can be identified in the process of synchronization. To demonstrate the validity of the proposed method, several illustrative examples are presented.

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Section: The Impact Of Fractional Order On the Identification Processmentioning

confidence: 99%

Adaptive Synchronization of Fractional Neural Networks with Unknown Parameters and Time Delays

et al. 2014

Entropy

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“…It should be noted that the condition of the form (5) is only a sufficient condition and not a necessary condition for stability of nonlinear system (3) [27,37].…”

Section: Stability Analysismentioning

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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“…In [11] chaotic behaviors are found when α = (0.9, 0.9, 0.9). Moreover, in [28] and [43], it is found that for the parameters α = (0.985, 0.99, 0.98) and α = (0.8, 1, 0.9), respectively, fractional order Chen system can display chaotic attractors. Fractional Chen system (6), when (a, b, c) = (35,3,28), has three equilibrium points,…”

Section: Fractional Chen Systemmentioning

confidence: 99%

“…Now, according to stability results and the results presented in [43], a necessary condition for fractional Chen system to exhibit chaotic attractors similar to its integer order counterpart is:…”

Section: Fractional Chen Systemmentioning

confidence: 99%

Adaptive feedback control and synchronization of non-identical chaotic fractional order systems

Odibat

2009

Nonlinear Dyn

152

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To cite this version:Zaid M. Odibat. Adaptive feedback control and synchronization of non-identical chaotic fractional order systems. Nonlinear Dynamics, Springer Verlag, 2009, 60 (4) Abstract This paper addresses the reliable synchronization problem between two non-identical chaotic fractional order systems. In this work, we present an adaptive feedback control scheme for the synchronization of two coupled chaotic fractional order systems with different fractional orders. Based on the stability results of linear fractional order systems and Laplace transform theory, using the master-slave synchronization scheme, sufficient conditions for chaos synchronization are derived. The designed controller ensures that fractional order chaotic oscillators that have nonidentical fractional orders can be synchronized with suitable feedback controller applied to the response system. Numerical simulations are performed to asses the performance of the proposed adaptive controller in synchronizing chaotic systems.

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Chaotic attractors in incommensurate fractional order systems

Cited by 317 publications

References 38 publications

Adaptive Synchronization of Fractional Neural Networks with Unknown Parameters and Time Delays

Adaptive Synchronization of Fractional Neural Networks with Unknown Parameters and Time Delays

Dynamics analysis of fractional order Yu-Wang system

Adaptive feedback control and synchronization of non-identical chaotic fractional order systems

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