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...

In this paper, we rigorously prove the existence and stability of asymmetric spotty patterns for the Gray-Scott model in a bounded two dimensional domain. We show that given any two positive integers k 1 ; k 2 , there are asymmetric solutions with k 1 large spots (type A) and k 2 small spots (type B). We also give conditions for their location and calculate their heights. Most of these asymmetr...

We performed a comprehensive study of the spike autosolitons: self-sustained solitary inhomogeneous states, in the classical reaction-diffusion system — the GrayScott model. We developed singular perturbation techniques based on the strong separation of the length scales to construct asymptotically the solutions in the form of a one-dimensional static autosolitons, higher-dimensional radially-s...

We performed a comprehensive study of spike autosolitons: highly localized solitary states, in the classical reaction-diffusion system — the Gray-Scott model. We developed singular perturbation techniques based on the strong separation of length scales to construct asymptotically the solutions in the form of one-dimensional and higher-dimensional radially-symmetric static autosolitons, and two ...