Discontinuous nonequilibrium phase transitions in a nonlinearly pulse-coupled excitable lattice model

Details Discontinuous nonequilibrium phase transitions in a nonlinearly pulse-coupled excitable lattice model Discontinuous nonequilibrium phase transitions in a nonlinearly pulse-coupled excitable lattice model

2009-10-29

arxiv.org/abs/0910.5717v2

Phys. Rev. E 80, 061105 (2009)

Nonlinear Sciences

Cellular Automata and Lattice Gases

8 pages, 6 figures

Scientific paper

10.1103/PhysRevE.80.061105

We study a modified version of the stochastic susceptible-infected-refractory-susceptible (SIRS) model by employing a nonlinear (exponential) reinforcement in the contagion rate and no diffusion. We run simulations for complete and random graphs as well as d-dimensional hypercubic lattices (for d=3,2,1). For weak nonlinearity, a continuous nonequilibrium phase transition between an absorbing and an active phase is obtained, such as in the usual stochastic SIRS model [Joo and Lebowitz, Phys. Rev. E 70, 036114 (2004)]. However, for strong nonlinearity, the nonequilibrium transition between the two phases can be discontinuous for d>=2, which is confirmed by well-characterized hysteresis cycles and bistability. Analytical mean-field results correctly predict the overall structure of the phase diagram. Furthermore, contrary to what was observed in a model of phase-coupled stochastic oscillators with a similar nonlinearity in the coupling [Wood et al., Phys. Rev. Lett. 96, 145701 (2006)], we did not find a transition to a stable (partially) synchronized state in our nonlinearly pulse-coupled excitable elements. For long enough refractory times and high enough nonlinearity, however, the system can exhibit collective excitability and unstable stochastic oscillations.

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