Abstract:

We mainly studied the instability of homogeneous steadystate solution to the attractiverepulsive KellerSegel model arising chemotaxis. We firstly linearized the system and argued the finite dimensional system including only one parameter. Finally, we proved the sufficient conditions for destabilization using the theory of nonnegative matrix and graph.

Key words: instability, pattern formation, KellerSegel model, morphogenesis, eigenvalue problem