An efficient simulation of the fractional chaotic system and its synchronization

Su, Daliang; Bao, Weimin; Liu, Jie; Gong, Chunye

doi:10.1016/j.jfranklin.2016.10.045

Cited by 11 publications

(8 citation statements)

References 29 publications

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“…Yeong-Jeu Sun 1 , Jer-Guang Hsieh 2 1 Professor, 2 Chair Professor Electrical Engineering, I-Shou University, Kaohsiung he concept of generalized stabilization for nonlinear systems is introduced and the stabilization of the generalized Liu chaotic control system is explored. Based on the time-domain approach with differential inequalities, a suitable uch that the generalized stabilization for a class of Liu chaotic system can be achieved.…”

Section: Chaos Suppression and Stabilization Of Generalized Liu Chaotmentioning

confidence: 99%

“…It is well known that the system (1) without any control (i.e., ( ) 0 = t u ) displays chaotic behavior for certain values of the parameters [1]. The paper is to search a novel control for the system (1) such that the generalized stability of the controlled system can be guaranteed. In this concept of generalized stabilization will be introduced.…”

Section: Roblem Formulation and Mainmentioning

confidence: 99%

“…, and It is well known that the system (1) without ) displays chaotic behavior for he aim of this for the system (1) of the feedback-In this paper, the stabilization will be domain approach with suitable control strategy will a control such stabilization of system (1) can be Let us introduce a definition which will be used in…”

Section: Theoremmentioning

confidence: 99%

“…In recent years, chaotic dynamic systems have been widely investigated by researchers; see, for instance, [1][2][3][4][5][6][7][8][9][10][11][12] and the references therein. Very often, chaos in many dynamic systems is an origin of the generation of oscillation and an origin of instability.…”

Section: Introductionmentioning

confidence: 99%

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Chaos Suppression and Stabilization of Generalized Liu Chaotic Control System

Sun¹,

Hsieh²

2018

IJTSRD

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In this paper, the concept of generalized stabilization for nonlinear systems is introduced and the stabilization of the generalized Liu chaotic control system is explored. Based on the time approach with differential inequalities, a suitable control is presented such that the generalized stabilization for a class of Liu chaotic system can be achieved. Meanwhile, not only the guaranteed exponential convergence rate can be arbitrarily pre specified but also the critical time can be correctly estimated. Finally, some numerical simulations are given to demonstrate the feasibility and effectiveness of the obtained results.

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Section: Chaos Suppression and Stabilization Of Generalized Liu Chaotmentioning

confidence: 99%

Section: Roblem Formulation and Mainmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Chaos Suppression and Stabilization of Generalized Liu Chaotic Control System

Sun¹,

Hsieh²

2018

IJTSRD

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“…The chaotic systems studied in fractional calculus are numerous in literature. [19][20][21][22][23][24] A fractional chaotic model and its application to chaotic system have been discussed in the work of Atangana. 24 A fractional model with no-indexed law and its application to chaos and statistics have been considered in the work of Atangana and Go´mez-Aguilar.…”

Section: Introductionmentioning

confidence: 99%

The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators

Khan

2019

Advances in Mechanical Engineering

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The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo–Fabrizio and the Atangana–Baleanu derivatives. Initially, we consider a new chaotic model and present some of the fundamental properties of the model. Then, we apply the Caputo–Fabrizio derivative and implement a numerical procedure to obtain their graphical results. Further, we consider the same model, apply the Atangana–Baleanu operator, and present their analysis. The Atangana–Baleanu model is used further to present a numerical approach for their solutions. We obtain and discuss the graphical results to each operator in details. Furthermore, we give a comparison of both the operators applied on the new chaotic model in the form of various graphical results by considering many values of the fractional-order parameter [Formula: see text]. We show that at the integer case, both the models (in Caputo–Fabrizio sense and the Atangana–Baleanu sense) give the same results.

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