Analytical and Numerical Study of the Projective Synchronization of the Chaotic Complex Nonlinear Systems with Uncertain Parameters and Its Applications in Secure Communication

Abstract

The main aim of this research is to find an analytical and numerical study to investigate the projective synchronization of two identical or nonidentical chaotic complex nonlinear systems with uncertain parameters. The secure communication between these systems is achieved based on this study. Based on the adaptive control technique and the Lyapunov function a scheme is designed to achieve projective synchronization of chaotic attractors of these systems. The projective synchronization of two identical complex Chen systems and two different chaotic complex Lü and Lorenz systems is taken as two examples to verify the feasibility of the presented scheme. These chaotic complex systems appear in several applications in physics, engineering, and other applied sciences. Numerical simulations are calculated to demonstrate the effectiveness of the proposed synchronization scheme and verify the theoretical results. The above results will provide theoretical foundation for the secure communication applications based on the proposed scheme.

A study of synchronization processes of nonlinear systems in the difference space of phase variables

“…In [7] there is given an analysis of the so-called "projective synchronization" on the example of Liu system. Herewith, there is introduced a special scale factor that helps analyze the possible synchronization error, caused by a linear combination of variables of the main and controlled systems, the behaviour of which can be nonlinear.…”

Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters

“…Apparently, the theoretical results in [15,31] are the special cases of our scheme. It should be noted that the feedback control gain in practical applications is desired as small as possible; however, the theoretical feedback control gains in [15,31] are fixed values no matter where the initial values start; thus, the gains must be larger than the values needed, which means a kind of waste in practice. In our method, we use an adaptive controller to overcome the above drawbacks.…”

Hybrid time-varying delay projective synchronization in complex dynamical networks

“…Zhang et al (2013) developed modified projective synchronization and Liu et al (2014) developed modified projective synchronization between different fractional-order systems. Abualnaja and Mahmoud (2014) developed projective synchronization for chaotic complex non-linear systems, and other projective synchronizations have been investigated (Agrawal and Das, 2014;Boulkroune and Mohammed, 2011;Farivar et al, 2012;Ghosh and Banerjee, 2013;Khan and Poria, 2013;Li et al, 2014;Luo and Wang, 2013;Mahmoud et al, 2013;Nian et al, 2013aNian et al, , 2013bOjo et al, 2013).…”