Fractional modified Duffing–Rayleigh system and its synchronization
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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.
KeywordsModified Duffing–Rayleigh oscillator Melnikov function method Fractional-order Synchronization
This work was supported by Grants from the National Natural Science Foundation of China (Nos. 11526109, 61379021), Natural Science Foundation of Fujian (Nos. 2015J05011, 2016J01671, JK2014028, JA14200), and the outstanding youth foundation of the Education Department of Fujiang Province.
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