【摘要】 研究了一种含有绝对值项的三维微分动力系统,用李雅普诺夫方法得到了系统发生第一次Hopf分岔的条件.利用相轨迹图、分岔图、最大李雅普诺夫指数谱等非线性动力学分析方法,分析了该系统从规则运动转化到混沌运动的规律.该系统是按照Feigenbaum途径(倍周期分岔)通向混沌的,在混沌区域存在周期窗口.当参数达到激变临界点时,混沌吸引子和不稳周期轨道在吸引子边界上碰撞,发生边界激变,激变临界值的领域内还存在相对长时间的瞬态混沌过程.更多还原

【Abstract】 This paper investigated a simple three dimensional nonlinear differentiable dynamical system with an absolute value term,whose boundary condition of the first Hopf bifurcation was derived by the Lyapunov method.Nonlinear dynamics techniques,such as phase portrait,bifurcation diagram and largest Lyapunov exponent spectrum,were employed to analyze the bifurcation and chaos features of the system.The chaotic patterns of the system were found to be resulted from Feigenbaum route,and the period windows existed inside the chaos region.When the controlling parameter passes the crisis critical value,the unstable periodic trajectory encounters with the chaotic attractor on the attractor’s boundary,which results in boundary crisis.Transient chaos also occurs during a relative long time,when the parameter,during a little range,is bigger than the crisis critical value.更多还原