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中文摘要：
利用Melnikov方法，分析了含有5次方恢复系数项的Φ^6-Duffing-van der Pol振子系统在单势阱参数条件下产生Smale意义下的混沌的必要条件.通过Poincar啨截面图、分岔图、Lyapunov指数谱和Lyapunov维数等理论和数值方法，阐明了系统运动在单势阱参数下随周期激励信号变化的动态特性、复杂性和系统的非线性特征.
英文摘要：
The necessary condition for the existence of chaotic behaviors in the sense of Smale in a Ф^6-Duffing-van der Pol oscillator, which has a 5th power nonlinear resilience item, is analyzed and determined by using the Melnikov method. The dynamic characteristic, complexity and the nonlinear dynamics characteristic of the O6 -DVP oscillator with single-well parameters is investigated by theoretical analysis and numerical simulation with the tiny change of the external forced excitation, the results are demonstrated by the Poincaré maps,bifurcation, Lyapunov-exponent spectrum, Lyapunov dimension and so forth.
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