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.
Lina Zhang. Shengmao Fu. "Nonlinear Instability for a Leslie-Gower Predator-Prey Model with Cross Diffusion." Abstr. Appl. Anal. 2013 (SI42) 1 - 13, 2013. https://doi.org/10.1155/2013/854862