On the Hyperchaotic Complex Lü System

Mahmoud, Gamal M.; Ahmed, Mansour E.; Mahmoud, Emad E.

doi:10.1142/9789814271349_0026

Cited by 16 publications

(32 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nearly all the 4D hyperchaotic systems, reported up to now, have double-wing hyperchaotic attractors with three or five equilibrium points [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Generating a hyperchaotic attractor from a smooth dynamical system with one equilibrium point is a very rare phenomenon [31,40,41].…”

Section: Introductionmentioning

confidence: 99%

Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form

Dadras

Momeni

et al. 2011

Nonlinear Dyn

View full text Add to dashboard Cite

In this paper, a new simple 4D smooth autonomous system is proposed, which illustrates two interesting rare phenomena: first, this system can generate a four-wing hyperchaotic and a four-wing chaotic attractor and second, this generation occurs under condition that the system has only one equilibrium point at the origin. The dynamic analysis approach in the paper involves time series, phase portraits, Lyapunov exponents, bifurcation diagram, and Poincaré maps, to investigate some basic dynamical behaviors of the proposed 4D system. The physical existence of the fourwing hyperchaotic attractor is verified by an electronic circuit. Finally, it is shown that the fractional-order S. Dadras · H.R. Momeni ( ) Automation and Instruments Lab, form of the system can also generate a chaotic fourwing attractor.

show abstract

Section: Introductionmentioning

confidence: 99%

Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form

Dadras

Momeni

et al. 2011

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…It is widely used in many fields of physics, engineering and secure communications [2,29,31]. Currently, more works have been done in the study of chaos and hyperchaos synchronization and many different kinds of synchronizations have been discovered such as completed synchronization, generalized synchronization, phase synchronization, projective synchronization, lag synchronization and impulsive synchronization [5,9,10,12,16,25,36], of most important, chaotic synchronization can be described as hybrid [14,30], high-dimension [4,19], fractional order [34], coupled complex system [17,18,35], and neural network [6,7].…”

Section: Introductionmentioning

confidence: 99%

Scaling Synchronization of a 6D Hyperchaotic System

Osman¹,

Zhu²,

Yang³

2018

dtcse

View full text Add to dashboard Cite

Abstract. This paper focuses on the scaling synchronization issue of a 6D hyperchaotic system with one or three equilibria which is obtained by controlling a 5D hyperchaotic system that is formed by adding a linear feedback controller and a nonlinear feedback controller to the Lorenz system. When the parameters are known in advance, applying the one-way linear coupling approach to synchronize the 6D hyperchaotic system up to a scaling factor. When the parameters are fully unknown, utilizing the adaptive method to synchronize the uncertain 6D hyperchaotic system up to a scaling factor. Finally, many numerical simulations have been carried out to verify the validation and efficiency of the proposed schemes.

show abstract

“…Recently, Mahmoud et al have designed and studied the complex Chen and complex Lü systems and showed their chaotic attractors and the stability properties of their fixed points [2]. A new hyperchaotic complex Lü system has constructed by adding a state feedback controller and using complex periodic forcing [3]. Another new chaotic complex nonlinear continuous system has been generated from the complex Lorenz system, and its dynamical properties has been also analyzed and studied [4].…”

Section: Introductionmentioning

confidence: 99%

Combination complex synchronization of three chaotic complex systems

et al. 2014

View full text Add to dashboard Cite

In this paper, we firstly design a chaotic complex system and study its dynamical properties including invariance, dissipativity, equilibria, Lyapunov exponents, chaotic behavior, as well as chaotic attractors. What is more, the scaling matrices are always chosen as real matrices in previous combination synchronization schemes within two drive real systems and one response real system evolving in the same or inverse directions simultaneously. However, in many real-life applications, the drive-response systems may evolve in different directions with a constant intersection angle. Therefore, combination synchronization with regard to the complex scaling matrices, referred as combination complex synchronization, will be made the further research about three chaotic complex systems. Based on Lyapunov stability theory, three identical chaotic complex systems are considered and the corresponding controllers are designed to achieve the complex combination synchronization. The corresponding theoretical proofs and numerical simulations are given to demonstrate the validity and feasibility of the presented control technique.

show abstract

On the Hyperchaotic Complex Lü System

Cited by 16 publications

References 0 publications

Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form

Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form

Scaling Synchronization of a 6D Hyperchaotic System

Combination complex synchronization of three chaotic complex systems

Contact Info

Product

Resources

About