Stability and Pattern Formation in a General Class of Reaction-Diffusion-Advection System

Abstract

This paper focuses on a general class of reaction-diffusion-advection system with linear cross-diffusion and cross-advection. By investigating the linearized stability of the constant equilibrium solution, we prove that the self-diffusion and self-advection terms have no effect on the stabilization of the constant steady state, the linear cross terms favor the destabilization of the constant steady state and mechanism of pattern formation. The theoretical results are applied to predator-prey and water-vegetation models with cross-diffusion and cross-advection.

Interspecific dispersal constraints suppress pattern formation in metacommunities

“…Furthermore, species may use both intra-and interspecific social cues when dispersing. Congregation behaviours may be reflected in directional biases in movement among patches that have been well studied in the context of animal grouping [21,58,59] and are known to facilitate spontaneous organization into heterogeneous patterns [10,[60][61][62]. Organisms may also emigrate from habitat patches in groups [63] and the cues used to synchronize group movements may include those from other species [3,15].…”