Dynamical Analysis Of A Class Of Predator-prey System With Diffussion

Due to widely existing in nature, predator-prey model plays an important rolein the field of exploration of the ecology and biology mathematics, At the sametime, predator-prey system has non-monotone structure, the research methods andtechnique are limited, In this paper, we study a class of predator-prey system withAllee effect and diffusion, and a detarled dynamical analysis of the conespondingparabolic systems is given; A prior of estimate and non-existence steady state so-lutions are obtained by using the regularity of elliptic equations; The stability oftrivial steady state solutions and the bifurcation of semitrivial steady state solutionare analyzed; Finally, the Hopf bifurcation of the parabolic equations is disscussed.