Qualitative Analysis Of A Class Of Diffusive Predator-Prey Systems With Age-Structure

As it is known, the predator-prey system is one of important tools to describe the nature. Since its equilibrium state can represent the long-term state of the nature, the study of stability of the predator-prey system is crucial. In this work, we focused mainly on stability of the predator-prey system containing of age structureand diffusion.Firstly, we proved the boundedness and permanence of solutions. Secondly,Linearization method and upper-lower solution method were used to obtain the conditions of equilibrium state in the predator-prey system and the local and global stability of the equilibrium points were discussed. In the last part of the work, the sufficient and necessary condition of zero stabilizability for the predator wasobtained by elliptic eigenvalue and comparison principle.