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中文摘要：
研究了具有同宿轨道、异宿轨道的双势阱Duffing振子在谐和激励与有界噪声摄动下的混沌运动．基于同宿分叉和异宿分叉，由Melnikov理论推导了系统出现混沌运动的必要条件及出现分形边界的充分条件．结果表明：当Wiener过程的强度参数大于某一临界值时，噪声增大了诱发混沌运动的有界噪声的临界幅值，相应地缩小了参数空间的混沌域，且产生混沌运动的临界幅值随着噪声强度的增大而增大。同时数值计算了最大Lyapunov指数，由最大Lyapunov指数为零从另一角度得到了系统出现混沌运动的有界噪声的临界幅值，发现在Wiener过程的强度参数大于某一临界值时，有界噪声的临界值也随着噪声强度的增大而增大，进一步用Poinearé截面研究了有界噪声对系统的影响，结果表明，当Wiener过程的强度参数小于某一临界值时。混沌吸引子扩散的面积随噪声强度的增大而有所增大。
英文摘要：
In this paper, the influence of harmonic and bounded noise excitations on the chaotic motion of a double well Duffing oscillator possessing both homoclinic and heteroclinic orbits is investigated. The criteria for occurrence of transverse intersection on the surface of homoclinic and heteroclinic orbits are derived by Melnikov theory, and are complemented by numerical calculations which display the bifurcation surfaces and the fractality of the basins of attraction. The results imply that the threshold amplitude of bounded noise for the onset of chaos moves upwards as the noise intensity increases beyond a critical value, which is further verified by numerically calculating the top Lyapunov exponents of the original system. Then we come to the conclusion that larger noise intensity results in smaller possible chaotic domain in the parameter space. The influence of bounded noise on Poinearé maps of the system response is also discussed, which indicates that when the noise intensity is less than some critical value, larger noise intensity results in larger area which the map occupies in the phase plane.
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