The universal law of the front speed close to the disappearance of bistability

Abstract

Multistable systems present rich dynamical behaviors of interfaces between the different equilibria. Close to the disappearance of bistability, i.e., transition between a bistable to a monostable region, we show that the speed of bistable fronts follows a square root law as a function of the bifurcation parameter. Analytically and numerically, we show this law for different prototype models of bistable systems. Based on a liquid crystal light valve experiment with optical feedback, we investigate the front speed close to the disappearance of bistability. Our results apply both to systems that do or do not follow energy minimization principles. Experimental findings show a quite fair agreement with the theoretical results.