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Robustness and asymptotic stability for the Winfree model on a general network under the effect of time-delay
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- Authors
- Issue Date
- 2018-11
- Publisher
- American Institute of Physics
- Citation
- Journal of Mathematical Physics, Vol.59 No.11, p. 112702
- Abstract
- We study the robustness and asymptotic stability of the unique equilibrium for the Winfree model on a general network under the effect of small time-delay. Time-delay is a ubiquitous mechanism in classical and quantum many-body systems, and it is due to the finite speed of communication. In this paper, we further investigate the robustness of the equilibrium under the effects of small time-delay and general network topology. For this, we present several sufficient frameworks formulated in terms of the network topology, coupling strength, time-delay, and initial configuration. In the proposed framework, we present a positively invariant arc which contains the unique equilibrium independent of strength of time-delay. By using energy estimates, we show that the unique equilibrium in the invariant arc is asymptotically stable. We also provide several numerical simulations and compare them with analytical results.
- ISSN
- 0022-2488
- Language
- English
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