A modified Turing model for the pattern formation model

The linear model introduced by Turing for pattern formation, known as the Turing bifurcation, is one of the most extensively studied mathematical programming problems in this field.\\ In this paper, we address a nonlinear reaction-diffusion model for pattern formation. Firstly, we demonstrate the bifurcation of this model in the Turing sense. Secondly, we employ a modified equation to stabilize the equations and investigate the instability of the Turing pattern. Finally, we provide several numerical test cases that validate the effectiveness of our modification.