Dynamics Of The Single Species Population Model In S~1

Climate change affects the habitat of living creatures.In order to adapt to this change,the species will move along with changes in the environment,where the migratory birds are a typical representative.In this paper,a reaction diffusion equation model with mobile response term is established in the annular region with the migratory phenomena of migratory birds on a loop year after year.Then,under the appropriate assumptions,analyzing the existence of traveling wave solution which is positive and periodic.The results show that the size of the velocity of the environment has a decisive influence on the existence of the traveling wave solutions.It is positive for research whether migratory birds can keep up with climate change.In this master thesis,the annular region is simplified into a ring,and the corresponding periodic traveling wave problem can be reduced to the periodic orbit problem of the planar system.Then,the phase plane analysis method is used to study the orbital properties of the model solution.Finally,for the reaction-diffusion model under the moving coordinates,we have carried on the numerical simulation,and the result is that the above-mentioned positive cycle line is obtained by the iterative method to obtain the existence of the positive traveling wave solution of the model.And the result suggests that the wave is unique and stable.