Chaos in the Newton–Leipnik system with fractional order

Sheu, Long-Jye; Chen, Hsien-Keng; Chen, Juhn-Horng; Tam, Lap Mou; Chen, Wen‐Chin; Lin, Kuang-Tai; Yuan, Kun

doi:10.1016/j.chaos.2006.06.013

Cited by 129 publications

(44 citation statements)

References 31 publications

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“…Theorem 1. Consider the fractional order SISO nonlinear system (10) with the control input (27), if the fuzzy-based adaptive laws are chosen as …”

Section: Stability Analysismentioning

confidence: 99%

“…In the last decade, a great number of research works focused on fractional systems that display chaotic behavior like: Chua circuit [6], Duffing system [7], Chen dynamic [8], characterization [9], Rössler system and Newton-Leipnik formulation [10]. Synchronization or control of these systems is a difficult task because a main characteristic of chaotic systems is their high sensitivity to initial conditions, but it is gathering more and more research effort due to several potential applications especially in cryptography [11].…”

Section: Introductionmentioning

confidence: 99%

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Chattering Elimination in Fuzzy Sliding Mode Control of Fractional Chaotic Systems Using a Fractional Adaptive Proportional Integral Controller

Khettab¹,

Bensafia²,

Ladaci³

2017

IJIES

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Abstract:In this paper, a Fractional Adaptive Fuzzy Logic Control (FAFLC) strategy based on active fractional sliding mode (FSM) theory is considered to synchronize chaotic fractional-order systems. Takagi-Sugeno fuzzy systems are used to estimate the plant dynamics represented by unknown fractional order functions. One of the main contributions in this work is to combine an adaptive fractional order PI λ control law with the fractional-order adaptive sliding mode controller in order to eliminate the chattering action in the control signal. Based on Lyapunov theory, the stability analysis of the proposed control strategy is performed for an acceptable synchronization error level. Numerical simulations illustrate the efficiency of the proposed fractional fuzzy adaptive control scheme through the synchronization of two different fractional order chaotic Duffing systems. We show that the introduction of the additional fractional adaptive PI λ control action is able to eliminate the chattering phenomena in the control signal.

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“…Theorem 1. Consider the fractional order SISO nonlinear system (10) with the control input (27), if the fuzzy-based adaptive laws are chosen as …”

Section: Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Chattering Elimination in Fuzzy Sliding Mode Control of Fractional Chaotic Systems Using a Fractional Adaptive Proportional Integral Controller

Khettab¹,

Bensafia²,

Ladaci³

2017

IJIES

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“…Some fractional-order differential systems, such as Duffing system [1] , Liu system [2] , Newton-Leipnik system [3] and so on, have been found. Their chaotic behaviors were presented.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Synchronization of Nonlinear-Coupled Fractional-order Liu System and Secure Communication

Xu¹

2015

Proceedings of the 2015 International Symposium on Computers &Amp; Informatics

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The synchronization of nonlinear-coupled fractional-order Liu systems is verified theoretically and numerically when the sum of the coupling coefficients of systems is 1 = + β α . Numerical simulations coincide with the theoretical analysis, and show fractional order and linear matrix influence chaotic synchronization. Furthermore, this method is applied in secure communication, and a chaotic masking system is designed.

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“…Motivated by potential applications in chaos synchronization , control chaotic dynamics has attracted significant interest . Some work has been done in the field of the chaos and control in fractional -order systems , including Chua system [1] , fractional-order Chen system [2] , fractional-order Lorenz system [3] , fractional-order Rossler system [4] and Newton -Leipnic system [5].…”

Section: Introductionmentioning

confidence: 99%

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2014

JCSCM

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Chaos in the Newton–Leipnik system with fractional order

Cited by 129 publications

References 31 publications

Chattering Elimination in Fuzzy Sliding Mode Control of Fractional Chaotic Systems Using a Fractional Adaptive Proportional Integral Controller

Chattering Elimination in Fuzzy Sliding Mode Control of Fractional Chaotic Systems Using a Fractional Adaptive Proportional Integral Controller

Chaotic Synchronization of Nonlinear-Coupled Fractional-order Liu System and Secure Communication

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