Two-Dimensional Manifolds with Computation V-Function of ODE Systems  

作　　者：Suqi Ma Bohan Ma Xinping Wang Suqi Ma;Bohan Ma;Xinping Wang(Department of Mathematics, China Agricultural University, Beijing, China;Department of Mechanics, Southwest Jiaotong University, Chengdu, China)

机构地区：[1]Department of Mathematics, China Agricultural University, Beijing, China [2]Department of Mechanics, Southwest Jiaotong University, Chengdu, China

出　　处：《International Journal of Modern Nonlinear Theory and Application》2023年第4期99-106,共8页现代非线性理论与应用（英文）

摘　　要：The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too.The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too.

关 键 词：Stable Manifold Unstable Manifold V-Function Attraction Boundary 

分 类 号：O17[理学—数学]