Synchronization of Two Rank‐One Chaotic Systems without and with Delay via Linear Delayed Feedback Control

Fang, Hui

doi:10.1155/2012/325131

Cited by 3 publications

(1 citation statement)

References 25 publications

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“…In 2009, Chen and Han studied the existence of rank one chaos in the neighborhood of a periodically kicked stable limit cycle close to a heteroclinic cycle of a planar equation [9]. In 2012, Fang studied the synchronization between rank one chaotic systems without and with delay using linear delayed feedback control method [10]. In 2013, Wang and Young gave a dynamical study of certain classes of rank one attractors [11].…”

Section: Introductionmentioning

confidence: 99%

Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay

Yang

Yong

Dai

2015

Discrete Dynamics in Nature and Society

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Rank one strange attractor in periodically kicked Lorenz system with time-delay is investigated. Our discussion is based on the theory of rank one maps formulated by Wang and Young. First, we develop the rank one chaotic theory to delayed systems. It is shown that strange attractors occur when periodically kicked delayed system undergoes a generic Hopf bifurcation. Then we use the theory to the periodically kicked Lorenz system with delay, and derivation of conditions for Hopf bifurcation and rank one chaos along with the results of numerical simulations are presented.

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Section: Introductionmentioning

confidence: 99%

Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay

Yang

Yong

Dai

2015

Discrete Dynamics in Nature and Society

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An overview of 0–1 test for chaos

Bernardini

Litak

2015

J Braz. Soc. Mech. Sci. Eng.

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Complete Synchronization of Strictly Different Chaotic Systems

Solı́s-Perales

2012

Journal of Applied Mathematics

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The criteria for complete synchronization of strictly different chaotic systems using feedback control are presented in this paper. Complete synchronization is achieved when all the states in the slave system are synchronous with the corresponding state in the master system. We illustrate that using a single input and single output control scheme, the synchronization of a class of strictly different systems is obtained in partial form. To overcome this problem we show that a multiple input and multiple output control scheme with an equal number of inputs and outputs than the order system is required in order to obtain the complete synchronization. This procedure is used to synchronize the Rössler and the Chen systems as an example. We also demonstrate that if the synchronization scheme considers less inputs and outputs, the partial-state synchronization is obtained.

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Synchronization of Two Rank‐One Chaotic Systems without and with Delay via Linear Delayed Feedback Control

Cited by 3 publications

References 25 publications

Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay

Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay

An overview of 0–1 test for chaos

Complete Synchronization of Strictly Different Chaotic Systems

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