A cross-diffusion prey-predator system exhibiting the prey group defense under homogeneous Neumann boundary conditions is studied.By considering the diffusive rate of the prey as a bifurcation parameter,we investigate...A cross-diffusion prey-predator system exhibiting the prey group defense under homogeneous Neumann boundary conditions is studied.By considering the diffusive rate of the prey as a bifurcation parameter,we investigate sudden changes in the population dynamics of the prey and predator which can have a substantial effect on population size of the species.First a priori estimate for positive steady states is obtained.Next we prove the existence of a pitchfork bifurcation of positive steady states at a simple eigenvalue.The structure of the global steady-state bifurcation is discussed.We also investigate the stability of the trivial solution line and nontrivial steady-state solutions via the eigenvalue perturbation theory.To illustrate our theoretical results some numerical simulations are given.Numerical examples contain a supercritical and a subcritical pitchfork bifurcation.展开更多
文摘A cross-diffusion prey-predator system exhibiting the prey group defense under homogeneous Neumann boundary conditions is studied.By considering the diffusive rate of the prey as a bifurcation parameter,we investigate sudden changes in the population dynamics of the prey and predator which can have a substantial effect on population size of the species.First a priori estimate for positive steady states is obtained.Next we prove the existence of a pitchfork bifurcation of positive steady states at a simple eigenvalue.The structure of the global steady-state bifurcation is discussed.We also investigate the stability of the trivial solution line and nontrivial steady-state solutions via the eigenvalue perturbation theory.To illustrate our theoretical results some numerical simulations are given.Numerical examples contain a supercritical and a subcritical pitchfork bifurcation.
