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

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 80; no. 6 Pt 1; p. 061105
• Main Authors: Assis, Vladimir R V, Copelli, Mauro
• Format: Journal Article
• Language: English
• Published: United States 01.12.2009
• Subjects: Algorithms; Computer Simulation; Models, Theoretical; Nonlinear Dynamics; Oscillometry - methods; Phase Transition
• ISSN: 1550-2376
• DOI: 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>or=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, 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.