2026/07/27 by Wenhai Shan, Xiao-Song Yang
paper · doi:10.1063/5.0321590
This paper investigates the stability and Turing instability of a migration-influenced two-species model. Based on the spectral analysis, we first consider how the chemotaxis affect the stability and instability of the linearized problem. Then, taking advantage of the ellipticity of the equation, using higher-order energy estimate, and imposing higher regularity constraints on the initial values, we further study the stability and instability for the nonlinear system in any dimensional space. Our theory not only eliminates the dimension limitation of the original theory (n ≤ 3), but also supplements the deficiency of the theory in the case of parabolic-elliptic coupling. Finally, we derive the amplitude equation by weakly nonlinear analysis, and verify the theoretical results by numerical simulation, revealing the transition between supercritical and subcritical bifurcation of competitive asymmetric regulation, and observing nonlinear phenomena such as hysteresis loop and bistable state.