Search

The anti-predator element because of fear from predator population in prey–predator models has an excellent significance and it is able to lessen the duplicate of prey population to a positive degree. In this paper, a delayed prey–predator model including fear effect and predator-taxis sensitivity is studied. Local stability and occurrence of Hopf bifurcation are analyzed by fixing the time delay as the bifurcating parameter. Then, a series of sufficient criteria for global stability is established by designing a suitable Lyapunov function. Furthermore, direction and stability of the Hopf bifurcation are studied. Lastly, numerical simulation outcomes are performed to confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

In this study, we present a delayed predator–prey model with cannibalism including a prey, a juvenile predator and an adult predator. The adult predator hunts not only the prey but also the juvenile predator. The alternative resource is considered to reduce cannibalism in predator species. The main results are demonstrated by local stability and Hopf bifurcation. Sufficient criteria for local stability of the interior equilibrium point and the exhibition of a Hopf bifurcation are derived. Global stability is analyzed via designing a suitable Lyapunov function. Additionally, stability of the Hopf bifurcation is explored. Finally, numerical simulations are executed to validate the obtained results. [ABSTRACT FROM AUTHOR]