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Phase-locking in k-partite networks of delay-coupled oscillators

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  • Singha, Joydeep
  • Ramaswamy, Ramakrishna

Abstract

We examine the dynamics of an ensemble of phase oscillators that are divided in k sets, with time-delayed coupling interactions only between oscillators in different sets or partitions. The network of interactions thus forms a k−partite graph. A variety of phase-locked states are observed; these include, in addition to the fully synchronized in-phase solution, splay cluster solutions in which all oscillators within a partition are synchronised and the phase differences between oscillators in different partitions are integer multiples of 2π/k. Such solutions exist independent of the delay and we determine the generalised stability criteria for the existence of these phase-locked solutions. With increase in time-delay, there is an increase in multistability, the generic solutions coexisting with a number of other partially synchronized solutions. The Ott-Antonsen ansatz is applied for the special case of a symmetric k−partite graph to obtain a single time-delayed differential equation for the attracting synchronization manifold. Agreement with numerical results for the specific case of oscillators on a tripartite lattice (the k=3 case) is excellent.

Suggested Citation

  • Singha, Joydeep & Ramaswamy, Ramakrishna, 2022. "Phase-locking in k-partite networks of delay-coupled oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001576
    DOI: 10.1016/j.chaos.2022.111947
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