Pal, S.; Al Basir, F.; Ray, S. Impact of Cooperation and Intra-Specific Competition of Prey on the Stability of Prey–Predator Models with Refuge. Math. Comput. Appl.2023, 28, 88.
Pal, S.; Al Basir, F.; Ray, S. Impact of Cooperation and Intra-Specific Competition of Prey on the Stability of Prey–Predator Models with Refuge. Math. Comput. Appl. 2023, 28, 88.
Pal, S.; Al Basir, F.; Ray, S. Impact of Cooperation and Intra-Specific Competition of Prey on the Stability of Prey–Predator Models with Refuge. Math. Comput. Appl.2023, 28, 88.
Pal, S.; Al Basir, F.; Ray, S. Impact of Cooperation and Intra-Specific Competition of Prey on the Stability of Prey–Predator Models with Refuge. Math. Comput. Appl. 2023, 28, 88.
Abstract
The main objective of this study is to find out the influence of cooperation and intra-specific competition in escaping predation through refuge of the prey population and the effect of the two intra-specific interactions on the dynamics of prey-predator systems. For this purposes, two mathematical models with Holling type-II functional response function have been proposed and analyzed. The first model includes cooperation among prey populations whereas the second one incorporates intra-specific competition. Existence conditions and stability of different equilibrium points of both models have been carried out for the qualitative behaviour of the systems. Refuge through intra-specific competition has a stabilizing role, whereas cooperation has a destabilizing role on the system dynamics. Periodic oscillations are observed in both the systems through Hopf bifurcation. From the analytical and numerical findings, we conclude that intra-specific competition affects the prey population and continuously checks the refuge class under a critical value, and thus it never becomes too large to cause predator extinction due to food scarcity. Conversely, cooperation leads maximum individuals to escape predation through the refuge so that predators will suffer from low predation success.
Keywords
Mathematical modeling; Bifurcation analysis; Global stability; Direction of Hopf bifurcation; Numerical simulations
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
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