| The dynamics behavior of the following diffusive density-dependent predator-prey model(?)is studied.We first discuss the existence,uniqueness and stability of positive equilibria of the corresponding ODE system.Then we analyze the large time behavior of time-dependent solution and stability of positive equilibria for the(*).Furthermore,the condition of Turing instability is obtained.Next we investigate the nonexis-tence/existence of nonconstant positive steady states.Finally,we taking d2 as a bifurcation parameter,the local bifurcation from positive equilibria is observed by using bifurcation theory,what’s more,the direction of the local bifurcation is stud?ied,then the local bifurcation can be extended to global bifurcation. |
