Hybrid synchronization of chaotic systems is a research problem with a goal to synchronize the states of master and slave chaotic systems in a hybrid manner, namely, their even states are completely synchronized (CS) and odd states are anti-synchronized. This paper deals with the research problem of hybrid synchronization of chaotic systems. First, a detailed analysis is made on the qualitative...

In this paper, a unified fuzzy H∞ control approach is proposed to deal with the problem of synchronization of two different hyperchaotic systems. The T–S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly. Based on the T–S fuzzy hyperchaotic models, a fuzzy H∞ synchronization controller is designed via parallel distributed...

Abstract. The control problem of a novel hyperchaotic system is investigated. The linear, speed, nonlinear, nonlinear doubly-periodic function feedback controls are used to suppress hyperchaos to unstable equilibrium. Limit cases of doubly-periodic function are considered and the hyperbolic function and trigonometric function feedback control laws are derived. The Routh–Hurwitz criterion is app...

This note points out that the assertions of [“Chen’s attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system,” CHAOS 23, 033108 (2013)] are groundless and incorrect. The failure of that criticism actually supports the strong standing of the Chen system.

This paper investigates the hybrid chaos synchronization of identical hyperchaotic Newton-Leipnik systems (Ghosh and Bhattacharya, 2010) by sliding mode control. The stability results derived in this paper for the hybrid chaos synchronization of identical hyperchaotic Newton-Leipnik systems are established using Lyapunov stability theory. Hybrid synchronization of hyperchaotic Newton-Leipnik sy...

In this paper, we introduce a new hyperchaotic complex T-system. This system has complex nonlinear behavior which we study its dynamical properties including invariance, equilibria and their stability, Lyapunov exponents, bifurcation, chaotic behavior and chaotic attractors as well as necessary conditions for this system to generate chaos. We discuss the synchronization with certain and uncerta...

In order to overcome sensitive defects of components deviations and environment defects in analog circuit design, a novel four-dimensional hyperchaotic systems is constructed based on LÜ system. Basic nonlinear dynamics characteristics are analyzed to the new system. By optimizing the design of sampling frequency selection, gain adjustments, parameter configuration etc., the hyperchaotic circui...

In this paper, the emergence of hyperchaos in a network with two very simple discrete periodic oscillators is presented. Uncoupled periodic oscillators may represent, in the crudest and simplest form, periodic oscillators in nature, for example fireflies, crickets, menstrual cycles of women, among others. Nevertheless, the emergence of hyperchaos in this kind of real-life network has not been p...

Anti-synchronization of chaotic systems is a research problem that deals with synchronizing the states of master and slave systems at a phase of 180 degrees, i.e. the states are equal in magnitude but opposite in sign. This paper deals with the anti-synchronization research problem of identical hyperchaotic Lü systems (Zhao and Lü, 2008) and new results are derived via sliding mode control. Thi...