Universal occurrence of the phase-flip bifurcation in time-delay coupled systems

Awadhesh Prasad, Syamal Kumar Dana, Rajat Karnatak, Juergen Kurths, Bernd Blasius, Ramakrishna Ramaswamy

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Abstract

Recently, the phase-flip bifurcation has been described as a fundamental transition in time-delay coupled, phase-synchronized nonlinear dynamical systems. The bifurcation is characterized by a change of the synchronized dynamics from being in-phase to antiphase, or vice versa; the phase-difference between the oscillators undergoes a jump of pi as a function of the coupling strength or the time delay. This phase-flip is accompanied by discontinuous changes in the frequency of the synchronized oscillators, and in the largest negative Lyapunov exponent or its derivative. Here we illustrate the phenomenology of the bifurcation for several classes of nonlinear oscillators, in the regimes of both periodic and chaotic dynamics. We present extensive numerical simulations and compute the oscillation frequencies and the Lyapunov spectra as a function of the coupling strength. In particular, our simulations provide clear evidence of the phase-flip bifurcation in excitable laser and Fitzhugh-Nagumo neuronal models, and in diffusively coupled predator-prey models with either limit cycle or chaotic dynamics. Our analysis demonstrates marked jumps of the time-delayed and instantaneous fluxes between the two interacting oscillators across the bifurcation; this has strong implications for the performance of the system as well as for practical applications. We further construct an electronic circuit consisting of two coupled Chua oscillators and provide the first formal experimental demonstration of the bifurcation. In totality, our study demonstrates that the phase-flip phenomenon is of broad relevance and importance for a wide range of physical and natural systems. (C) 2008 American Institute of Physics.

Original languageEnglish
Article number023111
Number of pages8
JournalChaos
Volume18
Issue number2
DOIs
Publication statusPublished - Jun 2008

Cite this

Prasad, A., Dana, S. K., Karnatak, R., Kurths, J., Blasius, B., & Ramaswamy, R. (2008). Universal occurrence of the phase-flip bifurcation in time-delay coupled systems. Chaos, 18(2), [023111]. https://doi.org/10.1063/1.2905146