The simultaneous effect of chemotaxis and alarm-taxis on the global existence and stability of a predator-prey system

Abstract: This study examines a fully parabolic predator-prey chemo-alarm-taxis system under homogeneous Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}<sup>n$ with a smooth boundary $\partial\Omega$. Under specific parameter conditions, it is shown that the system admits a unique, globally bounded classical solution. The convergence of the solution is established through the construction of an appropriate Lyapunov functional. In addition, numerical simulations are presented to validate the asymptotic behaviour of the solution. The results highlight the significant role of chemotaxis and alarm-taxis coefficients in determining the existence and stability of predator-prey models, as discussed in the literature.