Genetic differentiation of prey predator interaction model along with an Holling type-II functional response

Abstract

Prey–predator models play a vital role in mathematical biology. The competition that evolves between them is addressed in a broad scenario. According to genetics theory, various specie’s genotypes yield different outcomes in competition. This insight motivated us to introduce a genetic distinction between both predators and prey. The well-posedness of the system was determined for the proposed genetic variation prey–predator model in this research. With the use of equilibrium points, the model’s stability was examined using the center manifold theorem. Both local and global stability also proved for the system. Finally, numerical simulations are carried out with the suitable parameter values of the system.

Keywords

• Prey–predator model
• Equilibrium points
• Stability
• Center manifold theorem
• Bendixson–Dulac theorem
• Numerical methods