Detalle de: Complex Excitable Media: Activators Design, While Inhibitors Embellish

A system composed by coupled reaction–diffusion equations is one of the most classical scenarios of pattern formation. There are also other mechanisms of pattern formation, however, all have in common the interplay between a mechanism of transport and the nonlinearities of the system. Probably, the simplest example of pattern formation involving reaction–diffusion equations is a bistable front moving with constant velocity. A certain concentration U experiences an autocatalytic nonlinear growth and the corresponding increase of U travels along the media by diffusion. Such a process is simply modeled by a single reaction–diffusion equation. where F(U ) is a nonlinear function, typically a cubic function on U, giving rise to two stable solutions, i.e., bistable system. Under an adequate initial condition a front changes the stability from the metastable to the more stable solution. In such a case, the concentration U activates his own production and can be noted as activator. Such activation propagates by diffusion through the medium forming a traveling front with a fixed velocity which depends on the parameters on Eq. (1). The resulting fronts are robust and very stable waves which propagate through the system…