This work studies the stability and metastability of stationary patterns in a diffusionchemotaxis model without cell proliferation.We first establish the interval of unstable wave modes of the homogeneous steady state...This work studies the stability and metastability of stationary patterns in a diffusionchemotaxis model without cell proliferation.We first establish the interval of unstable wave modes of the homogeneous steady state,and show that the chemotactic flux is the key mechanism for pattern formation.Then,we treat the chemotaxis coefficient as a bifurcation parameter to obtain the asymptotic expressions of steady states.Based on this,we derive the sufficient conditions for the stability of one-step pattern,and prove the metastability of two or more step patterns.All the analytical results are demonstrated by numerical simulations.展开更多
基金Manjun Ma was supported by the National Natural Science Foundation of China(Nos.12071434 and 11671359).
文摘This work studies the stability and metastability of stationary patterns in a diffusionchemotaxis model without cell proliferation.We first establish the interval of unstable wave modes of the homogeneous steady state,and show that the chemotactic flux is the key mechanism for pattern formation.Then,we treat the chemotaxis coefficient as a bifurcation parameter to obtain the asymptotic expressions of steady states.Based on this,we derive the sufficient conditions for the stability of one-step pattern,and prove the metastability of two or more step patterns.All the analytical results are demonstrated by numerical simulations.
