Nonlinear Instability for a Leslie-Gower Predator-Prey Model with Cross Diffusion

Lina Zhang, Shengmao Fu
2013 Abstract and Applied Analysis  
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.
doi:10.1155/2013/854862 fatcat:xsrhziqvkzdrbad2nwcznnxqsu