Spatiotemporal complexity of a leslie-gower predator-prey model with the weak allee effect

We investigate a diffusive leslie-gower predator-prey model with the additive allee effect on prey subject to the zero-flux boundary conditions. some results of solutions to this model and its corresponding steady-state problem are shown. more precisely,we give the stability of the positive constant steady-state solution,the refined a priori estimates of positive solution,and the nonexistence and existence of the positive nonconstant solutions. we carry out the analytical study for two-dimensional system in detail and find out the certain conditions for turing instability. furthermore,we perform numerical simulations and show that the model exhibits a transition from stripe-spot mixtures growth to isolated spots and also to stripes. these results show that the impact of the allee effect essentially increases the model spatiotemporal complexity. © 2013 yongli cai et al.