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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Ф-Duffing-Van der Pol振子系统在单势阱参数条件下产生Smale意义下混沌的必要条件。通过Poincare截面图、分岔图、Lyapunov指数谱等理论和数值方法，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。最后，对单势阱参数条件下的中Ф^6-DVP振子的混沌自同步进行了进一步的研究，得到了很好的混沌同步控制结果。
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 Ф^6-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 demonstra- ted by the Poincar maps, bifurcation, Lyapunov-exponent spectrum and so forth. At last, the chaos self-synchronization in Ф^6-DVP oscillation is further studied, and the result of the chaos synchronization control is gained.
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