一种多涡卷蔡氏系统的混沌机理研究

Chaos Mechanism Analysis of a Multi-Scroll Chua System

通过修改蔡氏系统的非线性函数得到一种能产生多涡卷的变形蔡氏系统.分析了它的一些动力学特性,如分岔图和李氏指数.证明了系统的控制参数r在一个混沌区域变化时,其对应的Jacobin矩阵在平衡点的特征值都满足Shilnikov不等式.求解了混沌系统的Hopf分岔值并给出了相应证明.

By modifying the nonlinear function of Chua system,we obtain a new multi-scroll Chua system.We analyze some of its dynamics characteristics such as bifurcation diagram and Lyapunov-exponent.Then we prove that all the eigenvalues of the Jacobin matrices of the system at the fixed points satisfy the Shilnikov inequality when the control parameter ranges in the region of chaos.The Hopf bifurcation value of the system is solved and the corresponding proof is also given.