Asymptotic behavior of an age-structured prey-predator system with distributed delay

This paper devotes to the study on the asymptotic behavior of an age-structured prey-predator model with distributed delay. The existence of positive stationary solutions of the considered model is first discussed and the nonlinear system is linearized around a positive stationary solution. Then the resulting linear system is formulated as an abstract non-densely defined Cauchy problem so that the well-posedness is obtained for the system. Following that the problems of locally asymptotic stability/instability, asynchronous exponential growth as well as Hopf bifurcations for the linearized system are investigated with the help of operator semigroups theory and spectral analysis under some conditions. Finally, some numerical simulations are provided to illustrate the obtained results.