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2013
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# Grigory Osipov

## Publications:

 Grines E. A., Osipov G. V. Heteroclinic and Homoclinic Structures in the System of Four Identical Globally Coupled Phase Oscillators with Nonpairwise Interactions 2018, vol. 23, no. 7-8, pp.  974-982 Abstract Systems of $N$ identical globally coupled phase oscillators can demonstrate a multitude of complex behaviors. Such systems can have chaotic dynamics for $N > 4$ when a coupling function is biharmonic. The case $N = 4$ does not possess chaotic attractors when the coupling is biharmonic, but has them when the coupling includes nonpairwise interactions of phases. Previous studies have shown that some of chaotic attractors in this system are organized by heteroclinic networks. In the present paper we discuss which heteroclinic cycles are forbidden and which are supported by this particular system. We also discuss some of the cases regarding homoclinic trajectories to saddle-foci equilibria. Keywords: phase oscillators, heteroclinic networks Citation: Grines E. A., Osipov G. V.,  Heteroclinic and Homoclinic Structures in the System of Four Identical Globally Coupled Phase Oscillators with Nonpairwise Interactions, Regular and Chaotic Dynamics, 2018, vol. 23, no. 7-8, pp. 974-982 DOI:10.1134/S1560354718070110