基于复特征体系的线性系统动力学轨迹分析

Dynamical analysis of linear systems with complex eigensystem

针对具备复特征值的高维线性系统,探讨其基于特征体系的结构特征,并采用分解状态向量的方式将线性差分与线性微分系统的动力学轨迹行为特征进行对比分析.数值实验部分模拟了3种不同维度线性微分系统的解轨迹,具有复特征体系与仅具有实特征体系的动力学轨迹呈现出截然不同的行为特征,从而揭示出仅具备实特征体系的化学动力系统反应轨迹对于估计动力学参数的应用价值.

The structural characteristics of high-dimensional linear systems with complex eigenvalues are discussed.Meanwhile,the dynamic trajectory behavior characteristics of linear difference systems and linear differential systems are compared by means of decomposition of state vectors.In the numerical experiment section,the trajectories of three linear differential systems with different dimensions are simulated.The trajectories of systems with complex eigensystem and with only real eigensystem show that there are completely different behavior characteristics,which revealing the application value of reaction trajectories with only real eigensystem for estimating kinetic parameters.