一类非线性动力系统的混沌研究

Chaos Research on a Class of Nonlinear Dynamical Systems

对一类具有扰动作用的平面Hamilton动力系统进行了研究,讨论了该系统的异宿轨道和同宿轨道,并以实例给出系统发生混沌的临界条件·通过对含有二次和三次非线性项的具有扰动作用的平面Hamilton动力系统的研究,得出该系统在参数不同情况下的异宿轨道和同宿轨道及其产生的条件,最后利用Melnikov函数法以实例说明上述Hamilton动力系统发生混沌的临界条件·

Focusing on a class of nonlinear Hamilton dynamical systems, the heteroclinic and homoclinic orbits of this kind of nonlinear dynamical systems are discussed. Then, an example is given to demonstrate the critical conditions on that chaos occur. By studying the nonlinear Hamilton dynamical systems with second- and third-degree variables, heteroclinic and homoclinic orbits with different parameters are obtained, as well as their conditions. At last, an example is given to demonstrate the critical conditions on that the system enters chaos with Melnikov function method.