Fuhong Min

THE MECHANISM OF A CONTROLLED PENDULUM SYNCHRONIZING WITH PERIODIC MOTIONS IN A PERIODICALLY FORCED, DAMPED DUFFING OSCILLATOR

In this paper, the analytical conditions for the controlled pendulum synchronizing with periodic motions in the Duffing oscillator are developed using the theory of discontinuous dynamical systems. From the analytical conditions, the synchronization invariant domain is obtained. The partial and full synchronizations of the controlled pendulum with periodic motions in the Duffing oscillator are discussed. The control parameter map for the synchronization is achieved from the analytical conditions, and numerical illustrations of the partial and full synchronizations are carried out to illustrate the analytical conditions. This synchronization is different from the controlled Duffing oscillator synchronizing with chaotic motion in the periodically excited pendulum. Because the periodically forced, damped Duffing oscillator possesses periodic and chaotic motions, further investigation on the controlled pendulum synchronizing with complicated periodic and chaotic motions in the Duffing oscillator will be accomplished in sequel.

Complex Dynamics of Projective Synchronization of Chua Circuits with Different Scrolls

In this paper, the dynamics mechanism of the projective synchronization of Chua circuits with different scrolls is investigated analytically through the theory of discontinuous dynamical systems. The analytical conditions for the projective synchronization of Chua circuits with chaotic motions are developed. From these conditions, the parameter characteristics of the projective synchronization of Chua circuits with different scrolls are discussed, and the corresponding parameter maps and the invariant domain for such projective synchronization of Chua circuits are presented. Illustrations for partial and full projective synchronizations of the Chua circuits are given. The projective synchronization of Chua circuits is implemented experimentally, and numerical and experimental results are compared.

Chaotic Synchronization of a Controlled, Noised, Gyroscope System With an Expected Gyroscope System

In this paper, chaotic synchronization of a controlled, noised gyroscope system with an expected gyroscope system is investigated. From the theory of discontinuous dynamical systems, the necessary and sufficient conditions of such synchronization are presented. Numerical simulations for non-synchronization, partial and full chaotic synchronizations of two gyroscope systems are carried out.Copyright

Synchronization Dynamics of Two Gyroscope Systems

In this paper, the synchronization dynamics of two gyroscope systems is discussed by the theory of discontinuous dynamical systems. The necessary and sufficient conditions of such synchronization are obtained. The non-synchronization, partial and full synchronizations of two gyroscope systems are illustrated for the analytical conditions of synchronization.Copyright

The Synchronization of a Periodically Driven Pendulum With Periodic Motions in a Periodically Forced, Damped Duffing Oscillator

In this paper, the analytical conditions for the controlled pendulum synchronizing with periodic motions in Duffing oscillator is developed through the theory of discontinuous dynamical systems. The conditions for the synchronization invariant domain are obtained, and the partial and full synchronizations are illustrated for the analytical conditions.Copyright

Projective Synchronization of Two Gyroscope Systems with Different Motions

In this chapter, a simple nonlinear controller is applied to investigate the generalized projective synchronization for two gyroscopes with different dynamical behaviors. The projective synchronization conditions are developed through the theory of discontinuous dynamical systems. The synchronization invariant domain from the synchronization conditions is presented. The parameter maps are obtained for a better understanding of the synchronicity of two gyroscopes. Finally, the partial and full generalized projective synchronizations of two nonlinear coupled gyroscope systems are carried out to verify the effectiveness of the scheme. The scaling factors in such synchronization are observed through numerical simulations.

Chaotic Synchronization of Duffing Oscillator and Pendulum

The chaotic synchronization of the Duffing oscillator and controlled pendulum is investigated. The analytical conditions for the partial and full synchronizations of the controlled pendulum with chaotic motions in the Duffing oscillator are discussed. The partial and full synchronizations are illustrated to show the analytical conditions. This synchronization is different from the controlled Duffing oscillator synchronizing with chaotic motion in the periodically excited pendulum.

A generalized projective synchronization of two different gyroscopes

A generalized projective synchronization of a gyroscope with a chaotic gyroscope system is investigated under a nonlinear control law. The synchronization mechanism is developed from the theory of discontinuous dynamical systems. The generalized projective synchronization for two gyroscope systems can be achieved exactly in finite time, while the traditional methods of generalized projective synchronization only obtain asymptotic synchronization. The scaling factors in such synchronization are satisfied from numerical results.