We study two identical hyperchaotic oscillators symmetrically coupled. Each oscillator represents a codimension-2 Takens–Bogdanov bifurcation under square symmetry, and was used to model a convection experiment in a time-dependent state. In the coupled system, the Lyapunov exponents behavior against the coupling parameter is used to detect changes in the dynamics, and the synchronization state ...

A new controller design method is proposed to synchronize the fractional-order hyperchaotic system through the stability theory of fractional calculus; the synchronization between two identical fractional-order Chen hyperchaotic systems is realized by designing only two suitable controllers in the response system. Furthermore, this control scheme can be used in secure communication via the tech...

In this paper, based on Lyapunov stability theory, a scheme to realize finite-time hybrid synchronization of time-delay hyperchaotic Lorenz system is proposed. By theoretical analysis, the controllers are constructed. Finally, numerical simulations are given to verify the theoretical results.

Many methods have been proposed to synchronize chaotic systems. The most widely used methods are the continuous synchronization schemes [Pecora & Carroll, 1990], where the driving signals are transmitted continuously to the driven systems. The other synchronization schemes are impulsive synchronization [Panas et al., 1998] and selective synchronization [Itoh et al., 2000]. In an impulsive synch...

Synchronization scenarios of coupled mechanical metronomes are studied by means of numerical simulations showing the onset of synchronization for two, three, and 100 globally coupled metronomes in terms of Arnol'd tongues in parameter space and a Kuramoto transition as a function of coupling strength. Furthermore, we study the dynamics of metronomes where overturning is possible. In this case h...

The existence of rotatory, oscillatory, and oscillatory-rotatory synchronization of two coupled chaotic phase systems is demonstrated in the paper. We find four types of transition to phase synchronization depending on coherence properties of motions, characterized by phase variable diffusion. When diffusion is small the onset of phase synchronization is accompanied by a change in the Lyapunov ...

The problem of hybrid projective synchronization (HPS) strategies and control for the Baier–Sahle hyperchaotic flow in arbitrary dimensions with unknown parameters is considered. Based on the Lasalle invariance principle and adaptive control method, adaptive controllers and parameters update laws are given for the HPS between two identical hyper-chaotic systems with fully unknown parameters. Us...

The growth of technology and the emphasis on privacy have intensified the need to find a fast and secure cryptographic method. As chaotic signals are usually noise-like and chaotic systems are very sensitive to the initial condition, they can be used in cryptography. We have analyzed the properties of two new hyperchaotic systems that we have developed and then propose a secure chaotic cryptogr...

We investigate the detrimental effects of parameter mismatch on the synchronization of semiconductor lasers with electro-optical feedback, whose intensity dynamics can display a hyperchaotic behavior. Analytical techniques are developed to study the statistical properties of the synchronization error as a function of the various types of mismatches. The multiple mismatch case, which is of high ...