Stability and Turing bifurcation in a non-local reaction–diffusion equation with a top-hat kernel

In the non-local reaction–diffusion equation, the form of the kernel function has an important effect on the dynamics of the equation. In this paper, we study the spatiotemporal dynamics of a class of non-local reaction–diffusion equation where the non-locality is described by the top-hat function with the perceptual radius. The perceptual radius establishes a bridge between the local equation and global equation. It has been shown that the perceptual radius can destabilize the constant steady state via Turing bifurcation and the critical bifurcation value is theoretically determined.