摘要
提出了一种具有三维自治常微分方程组形式的新的类Chen系统,讨论了系统的基本动力行为以及吸引子的存在性,运用非线性系统理论和Routh-Hurwitz定理分别对系统平衡点的稳定性作了研究,得到了相关的定理.同时将系统在奇点处线性化,使得系统系数矩阵恰有一对共轭纯虚根和一个负实根,并在该平衡点处产生一个Hopf分支,然后利用Lyapunov方法和高维Hopf分支理论研究了系统的局部分叉特性,并通过二维中心流形定理详细对Hopf分叉和稳定性进行了分析和研究,获得了一些亚临界和超临界条件.最后通过数值示例进行仿真,对文中论述进行了强有力的验证.
A three-dimensional differential system derived from the Chen system was analyzed, whose basic dynamical behaviors and the existence of attractor based on the first Lyapunov coefficient were discussed. The stability of the equilibrium point of this system was studied using the nonlinear system theory and Routh-Hurwitz theorem, and the corresponding theorems were obtained. At the same time, the linearization of the system made the coefficient matrix of this system have a pair of purely imaginary conjugate roots and one negative real root, and bring a Hopf bifurcation on the equilibrium point. Then, the Lyapunov method and the high-dimensional Hopf bifurcation theory were applied to investigate the local bifurcation. And the bifurcation and stability were analyzed by the 2-dimensional local center manifold theorem, and some subcritical and supercritical conditions were obtained. Finally, the discussion was verified by numerical simulation.
出处
《动力学与控制学报》
2008年第1期16-21,共6页
Journal of Dynamics and Control
