We study a reaction-diffusion system which models the pre-mixed isothermal autocatalytic chemical reaction of order m (m > 1) between two species, reactant A and an auto-catalyst B, + B --> (m+1) linear decay -->C, where C is inert product. The special case = 2 much studied Gray-Scott model, but without feeding. prove existence multiple traveling waves have distinctive number local max...

Gray-Scott model has been studied extensively in recent years. However, most of the results are in one dimensional. In this paper, we study the 2-D Gray-Scott system. We rst construct two single pulse solutions and then we establish the stability and instability of such solutions in terms of the parameters involved.

In this work, we analyse a pair of two-dimensional coupled reaction-diusion equations known as the Gray-Scott model, in which spot patterns have been observed. We focus on stationary patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. A complete bifurcation study of these solutions is presented. The main mathematic...

This article focuses on the numerical solution of a classical, irreversible Gray Scott reaction-diffusion system describing kinetics simple autocatalytic reaction in an unstirred ow reactor. A novel finite element scheme based B-spline collocation method is developed to solve this model. Before applying method, "strang splitting" idea especially popularized for PDEs...

In this paper, we study in detail the existence and stability of localized pulses in a GiererMeinhardt equation with an additional ‘slow’ nonlinearity. This system is an explicit example of a general class of singularly perturbed, two component reaction-diffusion equations that goes significantly beyond wellstudied model systems such as Gray-Scott and Gierer-Meinhardt. We investigate the existe...

We give a complete classification of the phase portraits in Poincare´ disk for cubic polynomial systemsx˙=1−x−axy2,y˙=−by+axy2, R2 according with values its two parameters and b. These differential systems correspond to Gray-Scott model. Moreover we provide bifurcation diagram parameter plane (a,b) these systems.