Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis

Global existence of solutions and uniform persistence of a diffusive predator–prey model with prey-taxis

This paper proves the global existence and boundedness of solutions to a general reaction–diffusion predator–prey system with prey-taxis defined on a smooth bounded domain with no-flux boundary condition. The result holds for domains in arbitrary spatial dimension and small prey-taxis sensitivity coefficient. This paper also proves the existence of a global attractor and the uniform persistence...

Global Existence of Classical Solutions to a Three-Species Predator-Prey Model with Two Prey-Taxes

Predator-prey model with prey-taxis and diffusion

The objective of this paper is to investigate the effect of prey-taxis on predator–prey models with Paramecium aurelia as the prey and Didinium nasutum as its predator. The logistic Lotka–Volterra predator–prey models with prey-taxis are solved numerically with four different response functions, two initial conditions and one data set. Routh–Hurwitz’s stability conditions are used to obtain the...

The Dynamical Analysis of a Delayed Prey-Predator Model with a Refuge-Stage Structure Prey Population

A mathematical model describing the dynamics  of a  delayed  stage structure prey - predator  system  with  prey  refuge  is  considered.  The  existence,  uniqueness  and bounded- ness  of  the  solution  are  discussed.    All  the  feasibl e  equilibrium  points  are determined.  The   stability  analysis  of  them  are  investigated.  By  employ ing  the time delay as the bifurcation parame...

Permanence and global asymptotic stability of a delayed predator-prey model with Hassell-Varley type functional response

Here, a predator-prey model with Hassell-Varley type functional responses is studied. Some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable Lyapunov functional. Moreover, an example is illustrated to verify the results by simulation.