Compute 2D Stable and Unstable Manifolds of Nonlinear Maps
By using the fact that Jacobian transports derivative along the orbit of the invariant manifold, a new algorithm for computing 1D manifold is proposed first. The new mesh point is located with a Prediction-Correction scheme which reduces the searching time and at the same time gives rise to a simplified accuracy condition. Two dimensional manifold is computed by covering it with orbits of 1D sub-manifold. 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. The performance of the algorithm is demonstrated with hyper chaotic 3D Hénon map and Lorenz system.
KeywordsDerivative transportation Lorenz system Chaotic attractor
The work is supported by Tackle Key Problems in Science and Technology of The 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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