Nonlinear instability for a Leslie-Gower predator-prey model with cross diffusion (Q2319202)

Summary: A rigorous mathematical characterization for early-stage spatial and temporal patterns formation in a Leslie-Gower predator-prey model with cross diffusion is investigated. Given any general perturbation near an unstable constant equilibrium, we prove that its nonlinear evolution is dominated by the corresponding linear dynamics along a fixed finite number of the fastest growing modes.