摘要
The chaotic dynamic behaviors of a reduction of perturbed Korteweg-de Vries （KdV） equation in form of a parametric excitation are studied. Chaotic behaviors from homoclinic crossings are analyzed with an improved Melnikov method and are compared for the systems with a periodically external excitation, with a linear periodically parametric excitation, or with a nonlinear periodically excitation. The critical curves separating chaotic regions and non-chaotic regions of the above systems are different from each other. Especially, a dead frequency is presented for the system with a nonlinear periodically parametric excitation. The chaos excited at the frequency does not occur no matter how large the excitation amplitude is. A time integration scheme is used to find the numerical solutions of these systems. Numerical results agree with the analytical ones.
研究了具有参数激励约简的扰动KdV方程的混沌动力学行为。利用改进的Melnikov方法分析了由于同宿轨道的横截相交而产生的混沌行为。对周期外激励、周期线性参数激励和周期非线性参数激励下的扰动KdV方程的混沌行为进行了比较,发现划分混沌区与非混沌区的临界曲线是互不相同的。尤其是对非线性参数激励系统,存在"死频率"。当这类系统受到该频率激励时,不论激励的振幅多大,混沌也不会发生。用时间积分法对上述系统进行了数值计算,结果与理论分析一致。
基金
国家自然科学基金(10572057)资助项目
江苏省自然科学基金(BK2006186)资助项目~~
