On constructing simple examples of three-dimensional flows with multiple heteroclinic cycles
Tóm tắt
In this work we suggest a simple method for constructing G-equivariant systems of ODEs in ℝ3 (i.e., systems whose trajectories are invariant under the action of this group on ℝ3) that possess multiple disjoint heteroclinic networks. Heteroclinic networks under consideration consist of saddle equilibria that belong to coordinate axes and one-dimensional separatrices connecting them. We require these separatrices to lie on coordinate planes. We also assume the action of G on ℝ3 to be generated by cyclic permutation of coordinate variables and reflection with respect to one of the coordinate planes. As an example, we provide a step-by-step construction of three-dimensional flow with two disjoint heteroclinic networks. Also, we present a sketch of global dynamics analysis for the minimal example.
Tài liệu tham khảo
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