In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new fuzzy sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. Furthermore, three examples are presented to illustrate the effectiveness of the pr...

A method of synchronization is presented which, unlike existing methods, can, for generic dynamical systems, force all conditional Lyapunov exponents to go to -∞ . It also has improved noise immunity compared to existing methods, and unlike most of them it can synchronize hyperchaotic systems with almost any single coupling variable from the drive system. Results are presented for the Rossler h...

This paper addresses the hyperchaotification and the synchronization of chaotic systems. A nonlinear state feedback controller was designed to generate hyperchaos from the original chaotic system. The hyperchaos was identified by the existence of two positive Lyapunov exponents, bifurcation diagram and phase diagrams. Furthermore, effective active controllers are designed for synchronizing the ...

In this paper, experimental results on impulsive synchronization of two kinds of chaotic circuits; namely, Chua’s oscillator and a hyperchaotic circuit, are presented. To impulsively synchronize two Chua’s oscillators, synchronization impulses sampled from one state variable of the driving circuit are transmitted to the driven circuit. To impulsively synchronize two hyperchaotic circuits, synch...

We discuss the problem of the detection of hyperchaotic oscillations in coupled nonlinear systems when the available information about this complex dynamical regime is very limited. We demonstrate the ability of diagnosing the chaos-hyperchaos transition from return times into a Poincaré section and show that an appropriate selection of the secant plane allows a correct estimation of two positi...

Chimera states are particular trajectories in systems of phase oscillators with nonlocal coupling that display a spatiotemporal pattern of coherent and incoherent motion. We present here a detailed analysis of the spectral properties for such trajectories. First, we study numerically their Lyapunov spectrum and its behavior for an increasing number of oscillators. The spectra demonstrate the hy...

In this paper a general methodology for designing chaotic and hyperchaotic cryptosystems is developed. The basic idea is to make the decrypter a nonlinear observer for the state of the encrypter. Referring to this concept, some propositions are given which enable the plaintext to be retrieved if proper structural properties of the chaotic system hold. The proposed tool proves to be powerful and...

This paper presents anti-synchronization of two different chaotic systems using optimal control method. The proposed technique is applied to achieve chaos anti-synchronization for the new fourdimensional and hyperchaotic Lü systems with fully unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.