Computation of 2D Manifold Based on Generalized Foliation Condition
Stable and unstable manifolds play an important role in revealing the dynamics of dynamical systems. They form boundaries of different attractors and separate the whole space into different subspaces. Intersections of stable and unstable manifolds will lead to complexed dynamics, and homoclinic intersections are the source of chaos. A new algorithm for computing 2D stable and unstable manifolds of hyperbolic fixed points of maps is presented in this paper. A generalized Foliation Condition is used to guarantee that the 2D manifold is growing uniformly along the orbits of 1D sub-manifold in different directions. By foliation condition, the manifold has been better computed.
KeywordsDynamical system Map Stable manifold Unstable manifold
The work is supported by Tackle Key Problems in Science and Technology of He Nan province in China (Grant No. 112102210014), Tackle Key Problems in Science and Technology of Xinxiang city in China (Grant No. ZG11009).
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