Impulsive Control and Synchronization of Complex Lorenz Systems

Aly, Shaban; Al-Qahtani, Ali S.; Khenous, Houari B.; Mahmoud, Gamal M.

doi:10.1155/2014/932327

Cited by 7 publications

(7 citation statements)

References 31 publications

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“…In this article, we consider the discrete time approximated Lorenz system in the complex plane and we would like to compare the dynamics which has been already seen by others in the real and complex variables of the Lorenz system [17], [18], [19], [20], [21], [22], [23], [24], [25] and [26].…”

Section: Introductionmentioning

confidence: 99%

Computational Complex Dynamcs of the Discrete Lorenz System

Hassan¹

2019

JAND

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The dynamics of the classical Lorenz system is well studied in 1963 by E. N. Lorenz. Later on, there have been an extensive studies on the classical Lorenz system with the complex variables and the discrete time Lorenz system with real variables. To the best of knowledge of the author, so far there is no study on discrete time Lorenz system in complex variables. In this article, an attempt has been made to observe and understand the discrete dynamics of the Lorenz system with complex variables. This study compares the discrete dynamics of the Lorenz system with complex variables to that of the classical Lorenz system involving real and complex variables.• There are three fixed points of the Lorenz systems Eq.(3, 4, 5) and there are certain parameters r, a, and b (examples are given) such that the fixed points are stable (sink).• The system Eq.(3, 4, 5) possesses higher order periodic solutions too (few examples are given).• The system Eq.(3, 4, 5) has chaotic and transient chaotic solutions.• The system Eq.(3, 4, 5) has single and double coexisting chaotic attractors and existence of the chaotic attractors has been assured through examples.• A comparison have been made with other existing real and complex classical Lorenz systems.

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Section: Introductionmentioning

confidence: 99%

Computational Complex Dynamcs of the Discrete Lorenz System

Hassan¹

2019

JAND

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“…Recently, a number of control schemes have been developed to achieve various synchronization of memristor-based systems and complex systems. The adopted synchronization schemes include adaptive control [30][31][32], backstepping control [33], fuzzy control [8], impulsive control [34,35], etc. The realized synchronization types include complete synchronization [36,37], anti-synchronization [32], projective synchronization [23,38], lag synchronization [24,39], combination synchronization [40,41], compound synchronization [10], etc.…”

Section: Introductionmentioning

confidence: 99%

A Memristor-Based Complex Lorenz System and Its Modified Projective Synchronization

Wang

Zhou

2015

Entropy

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Abstract:The aim of this paper is to introduce and investigate a novel complex Lorenz system with a flux-controlled memristor, and to realize its synchronization. The system has an infinite number of stable and unstable equilibrium points, and can generate abundant dynamical behaviors with different parameters and initial conditions, such as limit cycle, torus, chaos, transient phenomena, etc., which are explored by means of time-domain waveforms, phase portraits, bifurcation diagrams, and Lyapunov exponents. Furthermore, an active controller is designed to achieve modified projective synchronization (MPS) of this system based on Lyapunov stability theory. The corresponding numerical simulations agree well with the theoretical analysis, and demonstrate that the response system is asymptotically synchronized with the drive system within a short time.

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“…As well all know, the synchronization and control on complex dynamical networks have attracted too many scientists' attention from various fields such as sociology, biology, mathematics and physics Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/neucom [14][15][16][17][18][19][20][21]. Although the well-studied sampled-data systems are similar to the complex dynamical networks with discrete-time communication, the theoretical results on the synchronization and consensus of the sampled-data systems cannot be usually analyzed if the network with discrete-time information interchanges directly.…”

Section: Introductionmentioning

confidence: 99%