Transition from homogeneous to inhomogeneous steady states in oscillators under cyclic coupling

Abstract

We report a transition from homogeneous steady state to inhomogeneous steady state in coupled oscillators, both limit cycle and chaotic, under cyclic coupling and diffusive coupling as well when an asymmetry is introduced in terms of a negative parameter mismatch. Such a transition appears in limit cycle systems via pitchfork bifurcation as usual. Especially, when we focus on chaotic systems, the transition follows a transcritical bifurcation for cyclic coupling while it is a pitchfork bifurcation for the conventional diffusive coupling. We use the paradigmatic Van der Pol oscillator as the limit cycle system and a Sprott system as a chaotic system. We verified our results analytically for cyclic coupling and numerically check all results including diffusive coupling for both the limit cycle and chaotic systems.

arXiv comment6 pages, 4 figures, published

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Cited by in corpus (4)

• Basin stability measure of different steady states in coupled oscillators
• Restoration of oscillation in network of oscillators in presence of direct and indirect interactions
• Emergent dynamics in delayed attractive-repulsively coupled networks
• Resurgence of oscillation in coupled oscillators under delayed cyclic interaction