Transition of Spatial Patterns in an Interacting Turing System

Abstract

We consider a Turing-type reaction-diffusion system involving quadratic and cubic nonlinearities and numerically investigate the role of nonlinear terms in producing spots, stripes, labyrinths, hexagonal arrangement of spots, blotches and transitions among them. From our numerical experiments performed on a square domain with zero-flux boundary conditions, we observe that the system displays a form of multistability for which different stable spatial distribution of concentrations appear for a same set of control parameters depending upon the initial conditions. For varying values of model parameters both in the first- and the second-stage of simulations, we obtain a number of transition states that are found to be sensitive on the relative strength of the quadratic and cubic coupling terms. We obtain a graphical relationship among such model parameters at which the transitions take place.