基于径向增长因子的二维不变流形计算

在计算二维不变流形时,为均衡各方向的增长速度,便于构建动力系统的全局流形结构,引入径向控制因子对原始动力学系统进行归一化.以流的切向量的径向分量为标准,控制其在径向的增长速度.理论分析和实例计算的结果均表明,归一化后的动力学系统和原始系统的流同轨,即全局流形结构一致.最后,通过对Lorenz和Duffing系统的流形计...

Computation of Two-dimensional Invariant Manifolds with Radial Growth Factor

In order to balance growth rate of manifold in all directions and construct global manifold structure of a dynamical system,a radial control factor is adopted to normalize the original dynamical system.Taking radius component of the tangent vector as a standard,this method controls manifold expanding at same speed in all directions.Theoretical analysis and example calculation demonstrate that manifolds before and after normalization have same orbit with the original one,which means their global manifold str...