Boundedness and Stabilization in a Stage-Structured Predator-Prey Model with Two Taxis Mechanisms

In this paper, we investigate a predator-prey system with stage structure for the predator under Neumann boundary condition, which has not only the taxis mechanism caused by the interaction between mature predator and prey, but also contains the taxis mechanism generated by the interaction between mature predator and immature predator. Regardless of the strength of the chemotactic coefficient, the existence and boundedness of global classical solutions are investigated for initial boundary value problems in two-dimensional space. In addition, appropriate Lyapunov functions are constructed to obtain the global asymptotic stability of the steady state solution under different predation intensity. In particular, it is interesting to observe that intra-specific competition keeps the species alive rather than dying out.