Dynamics of the light driven evolutionary models with chemotaxis

In the article we build a light-driven evolutionary model of Daphnia-Algae dynamic interaction. This interaction occurs through a reactive component and chemotaxis. The light-driven aspect of the process is modeled by space-time dependent coefficient which has periodic nature. Uniqueness and existence of the periodic equilibrium was proven under Dirichlet periodic boundary conditions. Sufficient condition of the Turing stability of the model near time-space dependent has a very clear intuitive interpretation.