Control of Population Size and Stability Through Diffusion: a Stage-Structure Model

Because of the ecological effects of human activities,many living and breeding areas of rana chensinensis were damaged and then the population size of rana chensinensis reduced rapidly. To analyze this phenomenon and to protect this well known economical species,two stage-structure models (1) and (2) of rana chensinensis dynamics are introduced and studied. In system (1),patch 1 and patch 2 are isolated each other in the sense that individuals can not move from one patch to another. But in system (2),some corridors were built between the two patches. Sufficient and necessary condition of permanent for system (2) be obtained in this paper. Further,we consider the effects of dispersal on the total population size and stability of positive equilibrium.