Synchronization and control of hyperchaotic complex Lorenz system

Mahmoud, Gamal M.; Mahmoud, Emad E.

doi:10.1016/j.matcom.2010.03.012

Cited by 79 publications

(52 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A hyperchaotic system is defined as an attractor with at least two positive Lyapunov exponents and an autonomous system with phase space of dimension at least four [8]. The sum of Lyapunov exponents must be negative to ensure that the system is dissipative [9]. The hyperchaotic systems have more complex structure, higher unpredictability, and more randomness than ordinary chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Analysis, Synchronization, Circuit Design, and Secure Communication of a Novel Hyperchaotic System

Liu

Zhang

2017

Complexity

View full text Add to dashboard Cite

This paper is devoted to introduce a novel fourth-order hyperchaotic system. The hyperchaotic system is constructed by adding a linear feedback control level based on a modified Lorenz-like chaotic circuit with reduced number of amplifiers. The local dynamical entities, such as the basic dynamical behavior, the divergence, the eigenvalue, and the Lyapunov exponents of the new hyperchaotic system, are all investigated analytically and numerically. Then, an active control method is derived to achieve global chaotic synchronization of the novel hyperchaotic system through making the synchronization error system asymptotically stable at the origin based on Lyapunov stability theory. Next, the proposed novel hyperchaotic system is applied to construct another new hyperchaotic system with circuit deformation and design a new hyperchaotic secure communication circuit. Furthermore, the implementation of two novel electronic circuits of the proposed hyperchaotic systems is presented, examined, and realized using physical components. A good qualitative agreement is shown between the simulations and the experimental results around 500 kHz and below 1 MHz.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamical Analysis, Synchronization, Circuit Design, and Secure Communication of a Novel Hyperchaotic System

Liu

Zhang

2017

Complexity

View full text Add to dashboard Cite

show abstract

“…It is well known that synchronization was proposed in 1990 [6]. Nowadays, synchronization of integer-order systems has been studied extensively and several methods are extended to synchronize fractional-order systems [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Design and analysis on Synchronization of a Fractional-order Bloch System

Liu¹

2017

Proceedings of the 2017 7th International Conference on Applied Science, Engineering and Technology (ICASET 2017)

View full text Add to dashboard Cite

Abstract. In this paper, the synchronization of a fractional-order Bloch system is investigated. Based on the stability theory of fractional-order systems, the scheme of synchronization for the fractional-order complex system is given. The synchronization of the system is realized by designing the appropriate controllers. Numerical simulations are used to demonstrate the effectiveness of the proposed scheme.

show abstract

“…Many new chaotic systems are found, then chaos control and chaos synchronization were researched. In recent years, researchers done much research on chaotic complex system (Mahmoud et al, 2011;Mahmoud and Mahmoud, 2010;Mahmoud et al, 2007;Mahmoud and Bountis, 2014). One of the chaotic complex system's researches is chaos synchronization.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Complex Projective Synchronization of Chaotic Complex System with disturbance

Zhang¹

2016

Revista de la Facultad de Ingeniería

View full text Add to dashboard Cite

We define a new synchronization method, adaptive complex projective synchronization, to real synchronization of two chaotic complex systems. The adaptive controller is obtained to make synchronization of two chaotic complex systems based on Lyapunov stability theory. This paper contribution is that make the scale function of projective synchronization is complex numbers. Numerical simulations are presented to illustrate the effectiveness of the proposed synchronization method.

show abstract

Synchronization and control of hyperchaotic complex Lorenz system

Cited by 79 publications

References 37 publications

Dynamical Analysis, Synchronization, Circuit Design, and Secure Communication of a Novel Hyperchaotic System

Dynamical Analysis, Synchronization, Circuit Design, and Secure Communication of a Novel Hyperchaotic System

Design and analysis on Synchronization of a Fractional-order Bloch System

Adaptive Complex Projective Synchronization of Chaotic Complex System with disturbance

Contact Info

Product

Resources

About