Pattern formation controlled by time-delayed feedback in bistable media

Abstract

Effects of time-delayed feedback on pattern formation are studied both numerically and theoretically in a bistable reaction-diffusion model. The time-delayed feedback applied to the activator and/or the inhibitor alters the behavior of the nonequilibrium Ising-Bloch (NIB) bifurcation. If the intensities of the feedbacks applied to the two species are identical, only the velocities of Bloch fronts are changed. If the intensities are different, both the critical point of the NIB bifurcation and the threshold of stability of front to transverse perturbations are changed. The effect of time-delayed feedback on the activator opposes the effect of time-delayed feedback on the inhibitor. When the time-delayed feedback is applied individually to one of the species, positive and negative feedbacks make the bifurcation point shift to different directions. The time-delayed feedback provides a flexible way to control the NIB bifurcation and the pattern formation. © 2010 American Institute of Physics.