Phase Synchronization Of Chaotic Systems Research Articles

Nonlinear observer based phase synchronization of chaotic systems

This Letter analyzes the phase synchronization problem of autonomous chaotic systems. Based on the nonlinear state observer algorithm and the pole placement technique, a phase synchronization scheme is designed. The phase synchronization of a new chaotic system is achieved by using this observer controller. Numerical simulations further demonstrate the effectiveness of the proposed phase synchronization scheme.

Phase synchronization of chaotic systems based on nonlinear observers

The phase synchronization problem of autonomous chaotic systems is discussod. Based on the nonlinear state observer algorithm and the pole placement technique, a phase synchronization scheme is designed. The phase synchronization of a new chaotic system is achieved by using this observer controller. Numerical simulations are carried out to verify its effectiveness.

Effect of noise on generalized chaotic synchronization

When two characteristically different chaotic oscillators are coupled, generalized synchronization can occur. Motivated by the phenomena that common noise can induce and enhance complete synchronization or phase synchronization in chaotic systems, we investigate the effect of noise on generalized chaotic synchronization. We develop a phase-space analysis, which suggests that the effect can be system dependent in that common noise can either induce/enhance or destroy generalized synchronization. A prototype model consisting of a Lorenz oscillator coupled with a dynamo system is used to illustrate these phenomena.

Phase synchronization of Chua circuit induced by the periodic signals

Phase synchronization of chaotic systems induced by periodic signals is studied experimentally and numerically. Three kinds of periodic signals are chosen to drive Chua circuits, including the periodic signal in the Chua circuit, sinusoidal and pulsed signals. Under conditions of small mismatch between the natural frequencies of the periodic and the chaotic signals, appropriate amplitudes of the driving signals and appropriate duty cycles of the pulse, phase synchronization can be achieved. Even when the duty circle reduces to 3{%}, it can still drive the chaotic signals into phase synchronization, which is interesting for applications.

Breaking a secure communication scheme based on the phase synchronization of chaotic systems.

A security analysis of a recently proposed secure communication scheme based on the phase synchronization of chaotic systems is presented. It is shown that the system parameters directly determine the cipher text waveform, hence it can be readily broken by system parameter estimation from the cipher text signal.

COHERENCE RESONANCE OF THE NOISE-INDUCED MOTION ON THE WAY TO BREAKDOWN OF SYNCHRONIZATION IN CHAOTIC SYSTEMS

We investigate the way in which noise destroys phase synchronization in chaotic systems. Two cases are considered: where the route to synchronization involves frequency locking; and where it occurs via a suppression of the natural dynamics. We show that, just as in the case of synchronization of periodic oscillations, noise induces a new motion whose coherence depends non-monotonically (resonantly) on the noise intensity.

A secure communication scheme based on the phase synchronization of chaotic systems.

Phase synchronization of chaotic systems with both weak and strong couplings has recently been investigated extensively. Similar to complete synchronization, this type of synchronization can also be applied in secure communications. We develop a digital secure communication scheme that utilizes the instantaneous phase as the signal transmitted from the drive to the response subsystems. Simulation results show that the scheme is difficult to be broken by some traditional attacks. Moreover, it operates with a weak positive conditional Lyapunov exponent in the response subsystem.

Phase synchronization of chaotic systems with small phase diffusion.

The geometric theory of phase locking between periodic oscillators is extended to phase coherent chaotic systems. This approach explains the qualitative features of phase locked chaotic systems and provides an analytical tool for a quantitative description of the phase locked states. Moreover, this geometric viewpoint allows us to identify obstructions to phase locking even in systems with negligible phase diffusion, and to provide sufficient conditions for phase locking to occur. We apply these techniques to the Rössler system and a phase coherent electronic circuit and find that numerical results and experiments agree well with theoretical predictions.