Steady state bifurcation of a population model with chemotaxis

In this paper, we are concerned with the pattern dynamics of a population model with chemotaxis. The existence of the solution and the global stability of the coexistence equilibrium are performed. In the sequel, we find that chemotaxis can induce the steady state bifurcation of the spatiotemporal model, and there are multiple thresholds of the steady state bifurcation with different assumptions. We then give the amplitude equation to determine the direction of the steady state bifurcation via the multiple time scales. It is found that the population model admits the supercritical or subcritical steady state bifurcation. Numerical results check the validity of the theoretical analysis.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this paper, the authors investigate the pattern dynamics of a population model with chemotaxis. They study the existence of solutions and the global stability of the coexistence equilibrium. The authors also explore the steady state bifurcation induced by chemotaxis in the spatiotemporal model, with multiple thresholds depending on different assumptions. They provide an amplitude equation to determine the direction of the steady state bifurcation and validate the theoretical analysis with numerical results.