Conference Paper

Dynamics of a two predator one prey model competing for the same prey with one predator having an advantage over the other

November 2022

Conference: International Conference on Nonlinear Analysis and Applications-2022

Authors:

B B Kishan College

Various ecological models have made significant contributions to improving our knowledge of prey-predator interactions. In this study, we develop a mathematical model of two predators feeding on a single prey species.We also consider that the two predator species engages in interspecific competition with each other for food and shelter as well as intraspecific competition among themselves. The predation functions for the two predators are considered to be the same and follows Holling Type-I functional response. We further suppose that one of the predators has an advantage over the other in terms of hunting strategy. All biologically viable equilibrium points are calculated analytically and numerically. The essential mathematical aspects of the model have been carefully examined in terms of stability and bifurcations arising in a few particular circumstances. To illustrate and support the analytical results, numerical simulations are performed.

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Coexistence of the Three Trophic Levels in a Model with Intraguild Predation and Intraspecific Compe...

November 2021 · Mathematical Biology and Bioinformatics

Evgeniya Giricheva

The model of a three-trophic community with intraguild predation is considered. The system consists of three coupled ordinary differential equations describing the dynamics of resource, prey and predator. Models with intraguild predation are characterized by predators that feed on resource of its own prey. A number of similar models with different functional responses have been proposed. In ... [Show full abstract] contrast to previous works, in the present model, the predator functional response to the resource is differed from that to the prey. The model takes into account an intraspecific competition of prey to stabilize the system in resource-rich environment. Conditions of existence and local stability of non-negative solutions are established. The possibility of Hopf bifurcation around positive equilibrium with consumption rate as bifurcation parameter is studied. For the model, in the plane of the consumption and predation rates, the regions of existence and stability of boundary and internal equilibria are constructed. Numerical simulations show that the region of equilibrium coexistence of populations is increased due to the inclusion of prey self-limitation in the model. Bifurcation diagrams confirm the stabilizing effect of intraspecific competition of prey on the system dynamics in resource-rich environment.

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A Beddington–DeAngelis type one-predator two-prey competitive system with help

October 2018 · Nonlinear Dynamics

In this paper, we present and study a two competing prey and one predator system where during predation both the teams of prey help each other and the rate of predation on both the teams are different. The prey consumption rate per individual of predator is considered as Beddington–DeAngelis type. Beddington–DeAngelis type functional response describes predator feeding rate depending on both the ... [Show full abstract] prey and predator density. Ecological significance of considering this type of functional response depends on how frequently a predator encounters another predator while feeding on the same type of prey, resulting in strong intraspecific competition and thereby reducing the predator feeding rate. Firstly we establish persistence and permanence of the system and examine the role of cooperation coefficient. Different conditions for the coexistence of equilibrium solutions are discussed. Then the local asymptotic stability of various equilibrium points and the existence of Hopf bifurcation at the positive equilibrium are carried out to understand the dynamics of the model system. The Kolmogorov analysis of subsystems suggests for the existence of transcritical bifurcation. Sufficient conditions for the nonexistence of periodic orbits of the considered model system have been presented. The analytical results found in this paper are illustrated with the help of numerical examples.