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

TL;DR

This study explores how nonlinear reinforcement in a stochastic SIRS model causes a shift from continuous to discontinuous phase transitions in various network structures, revealing complex collective behaviors.

Contribution

It introduces a nonlinear (exponential) contagion rate in the SIRS model, demonstrating the emergence of discontinuous phase transitions and bistability in excitable lattice systems.

Findings

Discontinuous phase transitions occur for strong nonlinearity in d≥2.

Hysteresis cycles and bistability characterize the transition.

No stable synchronization was observed despite similar nonlinear couplings.

Abstract

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.