Fractional modified Duffing-Rayleigh system and its synchronization.

Chaotic vibrations, stability and synchronization are important topics in nonlinear dynamics, and thus are studied in this paper for a new chaotic system with quadratic and cubic nonlinearly. The modified Duffing-Rayleigh system with piecewise quadratic function is presented firstly. Then, by taking the Melnikov function method, necessary conditions for chaotic motion of the modified Duffing-Rayleigh system are given. Fractional modified Duffing-Rayleigh oscillator is also discussed, and results of computer simulation demonstrate the chaotic dynamic behaviors of the fractional-order modified Duffing-Rayleigh system with order less than 2. Furthermore, generalized projective synchronization of two fractional modified Duffing-Rayleigh oscillators is explored by the active control technology. Adaptive synchronization and parameter identification of a fractional modified Duffing-Rayleigh oscillator with unknown parameters are also investigated. Numerical results validate the effectiveness and applicability of the proposed synchronization schemes. [ABSTRACT FROM AUTHOR]