Abstract

Spatially extended nonlinear systems often admit multiple coexisting stable states, and fronts connecting them are fundamental in the understanding of pattern formation. We are investigating the pinning of domain walls in a space-like dynamical system with delay with a view on using robust localized structures as bits in information storage and processing applications. However, in the simplest case of a symmetric bistable system with a single dynamical variable ψ, the stable coexistence between two phases is merely achieved for a single value of the parameters, the so-called Maxwell point. Such a regime possesses little experimental significance since any deviation of the control parameter or any symmetry breaking effect implies that one of the two bistable phases will eventually invade the other in a way reminiscent of nucleation bubbles in first order phase transitions. As such, the dynamics of the fronts separating the two phases and how they interact is of paramount importance. It is known that there exist strong analogies between spatially extended and delayed dynamical systems [1] and it was recently shown [2] that the same phenomenon of phase coarsening occurs in delayed bistables. Recently, additional attempts [3] were performed in order to try and pin the domain walls via an external temporal modulation.

© 2015 IEEE