Rich spatial-temporal dynamics in a diffusive population model for pioneer-climax species

摘要

A general diffusive population model for interactions of pioneer and climax species subject to the no-flux boundary condition is considered. Local and global steady-state bifurcations as well as Hopf bifurcations are investigated. A condition for Turing instability not to happen is obtained, and the conditions for occurrences of Turing bifurcations and Hopf bifurcations are also obtained. Numerical simulations are carried out to demonstrate and extend the obtained analytic results which suggest that the spatial diffusion may make the climax species more dominant. The results indicate that the model, with spatial diffusion incorporated , can have very rich spatial-temporal dynamics.