Dynamical behaviour of a delayed three species predator–prey model with cooperation among the prey species

2018 ◽  
Vol 92 (2) ◽  
pp. 627-643 ◽  
Author(s):  
Soumen Kundu ◽  
Sarit Maitra
Keyword(s):  
Prey Species ◽  
Dynamical Behaviour ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals A predator-prey model with disease in prey

2013 ◽  
Vol 18 (2) ◽  
pp. 191-209 ◽  
Author(s):  
Md. Sabiar Rahman ◽  
Santabrata Chakravarty
Keyword(s):  
Hopf Bifurcation ◽  
Prey Species ◽  
Dynamical Behaviour ◽  
Point Of View ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Prey Model ◽  
Predator Interactions ◽  
Disease In Prey

. The present investigation deals with the disease in the prey population having significant role in curbing the dynamical behaviour of the system of prey-predator interactions from both ecological and mathematical point of view. The predator-prey model introduced by Cosner et al. [1] has been wisely modified in the present work based on the biological point of considerations. Here one introduces the disease which may spread among the prey species only. Following the formulation of the model, all the equilibria are systematically analyzed and the existence of a Hopf bifurcation at the interior equilibrium has been duly carried out through their graphical representations with appropriate discussion in order to validate the applicability of the system under consideration

scholarly journals Coexistence for an Almost Periodic Predator-Prey Model with Intermittent Predation Driven by Discontinuous Prey Dispersal

2017 ◽  
Vol 2017 ◽  
pp. 1-15
Author(s):  
Yantao Luo ◽  
Long Zhang ◽  
Zhidong Teng ◽  
Tingting Zheng
Keyword(s):  
Growth Rates ◽  
Prey Species ◽  
Impulsive Differential Equations ◽  
Comparison Theorems ◽  
Almost Periodic ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Predator Prey Models

An almost periodic predator-prey model with intermittent predation and prey discontinuous dispersal is studied in this paper, which differs from the classical continuous and impulsive dispersal predator-prey models. The intermittent predation behavior of the predator species only happens in the channels between two patches where the discontinuous migration movement of the prey species occurs. Using analytic approaches and comparison theorems of the impulsive differential equations, sufficient criteria on the boundedness, permanence, and coexistence for this system are established. Finally, numerical simulations demonstrate that, for an intermittent predator-prey model, both the intermittent predation and intrinsic growth rates of the prey and predator species can greatly impact the permanence, extinction, and coexistence of the population.

The economics of fishing down the food chain

2002 ◽  
Vol 59 (5) ◽  
pp. 755-758 ◽  
Author(s):  
Rögnvaldur Hannesson
Keyword(s):  
Global Optimization ◽  
Open Access ◽  
Food Chain ◽  
Prey Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Desirable Effect

This paper uses a predator–prey model to discuss the fundamental economics of fishing down the food chain. Three regimes are compared: open access, global optimization, and partial optimization of rents from each stock. If the net price of prey species increases, fishing down the food chain would indeed be a desirable effect in economic terms. Under open access, however, fishing down the food chain could occur as a result of a higher net price of species higher up in the food chain. With partial optimization, there could be less fishing down the food chain than economically desirable.

scholarly journals A Holling–Tanner Predator–Prey Model with Strong Allee Effect

2019 ◽  
Vol 29 (11) ◽  
pp. 1930032 ◽  
Author(s):  
Claudio Arancibia-Ibarra ◽  
José D. Flores ◽  
Graeme Pettet ◽  
Peter van Heijster
Keyword(s):  
Allee Effect ◽  
Phase Plane ◽  
Prey Species ◽  
Basins Of Attraction ◽  
Extended Model ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Strong Allee Effect ◽  
Species Production

We analyze a modified Holling–Tanner predator–prey model where the predation functional response is of Holling type II and we incorporate a strong Allee effect associated with the prey species production. The analysis complements the results of previous articles by Saez and González-Olivares [1999] and Arancibia-Ibarra and González-Olivares [2015] discussing Holling–Tanner models which incorporate a weak Allee effect. The extended model exhibits rich dynamics and we prove the existence of separatrices in the phase plane separating basins of attraction related to coexistence and extinction of the species. We also show the existence of a homoclinic curve that degenerates to form a limit cycle and discuss numerous potential bifurcations such as saddle-node, Hopf, and Bogdanov–Takens bifurcations.

Permanence of a diffusive Leslie–Gower predator–prey model incorporating a prey refuge

2014 ◽  
Vol 07 (03) ◽  
pp. 1450027 ◽  
Author(s):  
Wensheng Yang
Keyword(s):  
Prey Species ◽  
Necessary Conditions ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Sufficient And Necessary Conditions

The diffusive Leslie–Gower predator–prey model incorporating a prey refuge is reconsidered here. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained, and our results supplement earlier ones.

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