Stability and metastability in a chemotaxis model

This work studies the stability and metastability of stationary patterns in a diffusion-chemotaxis 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.