Study on chaotic characteristics of horizontal nonlinear roller system with fractional order

摘要

Abstract In this paper, Duffing oscillator is introduced to study the chaotic characteristics of nonlinear roller system in detail. Firstly, the horizontal nonlinear dynamics equations of the roller system with fractional derivative terms were established . Secondly, amplitude–frequency characteristics of the system by the multi-scale method were solved and the influence relationship of various parameters on the system was discussed. Thirdly, according to the perturbation theory and the Melnikov method, the necessary conditions were studied for generating chaos under the Smale horseshoe meaning of the roller system. Finally, the coincidence of the analytical and numerical solutions was verified . And the chaotic characteristics of the system are studied by numerical simulation.