一类转子系统的非线性随机稳定性及随机Hopf分岔

Nonlinear Stochastic Stability and Stochastic Hopf Bifurcation of a Class of Rotor Systems

摘要: 本文主要分析一个随机参数激励下四维高速转子系统的非线性随机稳定性及随机Hopf分岔。转子系统动力学的研究在理论和实际操作也有了很大的进步。将系统受到的内部因素与外部随机风力影响用高斯色噪声代替。运用随机平均原理，将拟哈密顿系统收敛于一个一维伊藤随机扩散过程，然后运用最大李雅普诺夫指数法，来判断系统的局部稳定性，得到系统局部稳定的条件。然后通过FPK方程之解，即平稳概率密度来模拟系统发生Hopf分岔。

Abstract: This paper mainly analyzes the nonlinear random stability and random Hopf bifurcation of a four-dimensional high-speed rotor system under a random parameter excitation. The study of rotor system dynamics has made great progress in theory and practice. The system is affected by internal factors and external random wind and replaced by Gaussian color noise. By using the principle of random average, the quasi-hamiltonian system is convergent to a one-dimensional random ITO diffusion process, and then the maximum lyapunov exponential method is used to judge the local stability of the system, and the conditions for the local stability of the system are obtained. Then the Hopf bifurcation is simulated by the solution of FPK equation, namely the stationary probability density.