A general method for exploring three-dimensional chaotic attractors with complicated topological structure based on the two-dimensional local vector field around equilibriums

摘要

This paper proposed a new method for exploring three-dimensional chaotic attractors with complicated topological structure. Based on the index theory, the theoretical foundation of the new method is explained clearly and concisely, and the feasibility of this method is progressively illustrated by a multi-wing three-dimensional chaotic attractor derived from a two-dimensional continuous autonomous dynamical system with thirteen equilibrium points. Moreover, the experimental results are also discussed. To validate the generalization ability of the proposed method, another two chaotic systems are constructed based on the proposed method. The numerical results show the effectiveness of the proposed method.