| Abstract: |
| In this talk, we consider a predator-prey system with a certain type of prey-dependent diffusion for predators where the source of prey population depends on location in a habitat with spatial heterogeneity distributed within a bounded domain. It is assumed that the spread rate of predators can change depending on the satisfaction of predators according to the amount of available prey in the vicinity of predators in the habitat. We demonstrate that predators can invade a habitat region through prey-dependent diffusion by analyzing the stability of the system`s semitrivial solution when the predator is absent. We also explore the existence and uniqueness of a positive steady state using fixed point index theory in a positive cone in a Banach space. We conclude that the coexistence state is unique if the prey`s diffusion rate is above a specific threshold and the average of the prey`s resource function is within a particular range represented by the prey`s equilibrium value. |
|