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2013
Impact Factor

# Evgeny Grines

ul. Gagarina 23, Nizhni Novgorod, 606950 Russia
Nizhni Novgorod State University

## Publications:

 Grines E. A., Osipov G. V. On Constructing Simple Examples of Three-dimensional Flows with Multiple Heteroclinic Cycles 2015, vol. 20, no. 6, pp.  679-690 Abstract In this work we suggest a simple method for constructing $G$-equivariant systems of ODEs in $\mathbb{R}^3$ (i.e., systems whose trajectories are invariant under the action of this group on $\mathbb{R}^3$) 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 $\mathbb{R}^3$ 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. Keywords: heteroclinic cycle, heteroclinic network Citation: Grines E. A., Osipov G. V.,  On Constructing Simple Examples of Three-dimensional Flows with Multiple Heteroclinic Cycles, Regular and Chaotic Dynamics, 2015, vol. 20, no. 6, pp. 679-690 DOI:10.1134/S1560354715060040