Abstract

Bazykin’s prey–predator system with constant and adaptive prey refuge is investigated in this paper. We examine Bazykin’s resource consumer system with exponential growth rate and by employing constant prey refuge we demonstrate that refuge does promote species coexistence. The incorporation of constant prey refuge expands the stability zone for the interior equilibrium. Furthermore, the bifurcation diagram with reference to prey refuge (ur) shows how ur influences the system’s behavior from unstable to periodic stability and then to equilibrium stability. Next, we provide a Bazykin’s model with adaptive prey refuge and develop a fitness function for the prey population using refuge as a strategy and in order to obtain the prey’s optimal response to the environment we determine evolutionary stable strategies (ESS). Our model consists of more than one ESS, thus we employ the best response dynamics for the prey strategy. Our analysis showcases that adaptive refuge used by the prey population promotes the coexistence of prey–predator dynamics. Our theoretical analysis is supported by extensive numerical simulations. Bifurcation diagrams with reference to the two most crucial parameters, namely, δ2 (intra-species competition rate among predators) and τ (the rate at which populations adapt to their environment), are included in the numerical analysis. Species cohabitation along a limit cycle or at an equilibrium is discovered to be dependent on the pace of strategy dynamics and the competition amongst predator species.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.