Spreading and vanishing in a diffusive intraguild predation model with intraspecific competition and free boundary

2019 ◽  
Vol 42 (18) ◽  
pp. 6917-6943
Author(s):  
Dawei Zhang ◽  
Binxiang Dai
Keyword(s):  
Free Boundary ◽  
Intraspecific Competition ◽  
Intraguild Predation ◽  
Spreading And Vanishing

scholarly journals Coexistence of the Three Trophic Levels in a Model with Intraguild Predation and Intraspecific Competition of Prey

2021 ◽  
Vol 16 (2) ◽  
pp. 394-410
Author(s):  
Evgeniya Giricheva
Keyword(s):  
Intraspecific Competition ◽  
Intraguild Predation ◽  
Local Stability ◽  
Consumption Rate ◽  
Present Model ◽  
Trophic Levels ◽  
Positive Equilibrium ◽  
Functional Responses ◽  
Equilibrium Coexistence ◽  
Existence And Stability

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 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.

Global dynamics of delayed intraguild predation model with intraspecific competition

2018 ◽  
Vol 11 (08) ◽  
pp. 1850116
Author(s):  
Zhenzhen Li ◽  
Binxiang Dai
Keyword(s):  
Periodic Solution ◽  
Global Existence ◽  
Intraspecific Competition ◽  
Intraguild Predation ◽  
Critical Value ◽  
Existence Results ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
The Stability ◽  
Theoretical Results

A delayed intraguild predation (IGP) model with intraspecific competition is considered. It is shown that the delay has a destabilizing effect and induces oscillations. The global existence results of periodic solutions bifurcating from the positive equilibrium are established. It is shown that there exists at least one nontrival periodic solution when the delay passes through a certain critical value. Numerical simulations are performed to illustrate our theoretical results and show that intraspecific competition can also affect the stability of the positive equilibrium of the system.

scholarly journals A free boundary problem with a Stefan condition for a ratio-dependent predator-prey model

2021 ◽  
Vol 6 (11) ◽  
pp. 12279-12297
Author(s):  
Lingyu Liu ◽  
◽  
Alexander Wires ◽  
Keyword(s):  
Free Boundary ◽  
Moving Boundary ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Spreading And Vanishing ◽  
Prey Model ◽  
Whole Space ◽  
Ratio Dependent ◽  
Stefan Condition ◽  
A Free Boundary Problem

<abstract><p>In this paper we study a ratio-dependent predator-prey model with a free boundary caused by predator-prey interaction over a one dimensional habitat. We study the long time behaviors of the two species and prove a spreading-vanishing dichotomy; namely, as $ t $ goes to infinity, both prey and predator successfully spread to the whole space and survive in the new environment, or they spread within a bounded area and eventually die out. The criteria governing spreading and vanishing are obtained. Finally, when spreading occurs we provide some estimates to the asymptotic spreading speed of the moving boundary $ h(t) $.</p></abstract>

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