For dynamical systems possessing invariant subspaces one can have a robust homoclinic cycle to a chaotic set. If such a cycle is stable, it manifests itself as long periods of quiescent chaotic behaviour interrupted by sudden transient 'bursts'. The time between the transients increases as the trajectory approaches the cycle. This behavior for a cycle connecting symmetrically related chaotic se...

Chaos in nonlinear dynamics occurs widely in physics, chemistry, biology, ecology, secure communications, cryptosystems and many other scientific disciplines. Chaotic systems have many important applications in science and engineering. This paper derives new results for the analysis and adaptive control of a chemical chaotic attractor discovered by Haung (2005). This paper starts with a detaile...

In this paper, generalized synchronization (GS) is extended from real space to complex space, resulting in a new synchronization scheme, complex generalized synchronization (CGS). Based on Lyapunov stability theory, an adaptive controller and parameter update laws are designed to realize CGS and parameter identification of two nonidentical chaotic (hyperchaotic) complex systems with respect to ...

It is a hard problem to anticipate the dynamic characteristics of non-linear chaotic system. In this paper, based on a stability theorem proved for linear chaotic systems, a scheme for anticipating synchronization of chaotic system is proposed. This paper investigate the synchronization between the receiver system and the future state of a transmitter system for an arbitrarily long anticipation...

In the present paper we show that inhomogeneity of a continuous self-sustained oscillating medium can be a reason for the onset of chaotic behavior. It has been established that temporal chaotic dynamics typically arises in the medium with a linear mismatch of the natural frequency along a spatial coordinate, whereas a chaotic regime is not characteristic for the medium with randomly distribute...

In this paper, a scheme for chaotic modulation secure communication is proposed based on chaotic synchronization of an improved Lorenz system. For the first time, the intensity limit and stability of the transmitted signal, the characteristics of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. In addition, some improvements are made on ...

A chaotic system owns complex dynamics though it is with deterministic expression in mathematics, and it has attractived numerous study and application in many fields of the world. But for a concrete application, it is usually with parameters uncertainty while it is implemented. In this paper synchronization of discrete-time chaotic systems with parameters and/or structure uncertainty is resear...

We introduces a new method that can achieve the generation of Colpitts chaotic signal The system is based on virtual instrument platform and combined with MATLAB calculation to achieve the generation of Colpitts chaotic signal and making it analysis with autocorrelation and power spectrum at the same time. Signal channel output of chaotic signal was realized through USB-6009 acquisition module ...

Chaos may be degenerated because of the finite precision effect, hence, in this work, for given a new fractional order three-dimensional chaotic attractors, numerical investigations on the dynamics of this system have been carried out. The stability of equilibrium for the system is analyzed according to the qualitative theory. Furthermore, a new chaotic control technique is designed, the specia...