Dynamics of prey–predator model with strong and weak Allee effect in the prey with gestation delay

• Published in: Nonlinear analysis (Vilnius, Lithuania) Vol. 25; no. 3
• Main Authors: Kumar, Ankit, Dubey, Balram
• Format: Journal Article
• Language: English
• Published: Vilnius University Press 01.05.2020
• Subjects: Allee effect; gestation delay; Hopf-bifurcation; prey–predator models; Hopf-bifurcation; Allee effect; gestation delay; prey–predator models
• ISSN: 1392-5113; 2335-8963; 2335-8963
• DOI: 10.15388/namc.2020.25.16663

This study proposes two prey–predator models with strong and weak Allee effects in prey population with Crowley–Martin functional response. Further, gestation delay of the predator population is introduced in both the models. We discussed the boundedness, local stability and Hopf-bifurcation of both nondelayed and delayed systems. The stability and direction of Hopfbifurcation is also analyzed by using Normal form theory and Center manifold theory. It is shown that species in the model with strong Allee effect become extinct beyond a threshold value of Allee parameter at low density of prey population, whereas species never become extinct in weak Allee effect if they are initially present. It is also shown that gestation delay is unable to avoiding the status of extinction. Lastly, numerical simulation is conducted to verify the theoretical findings.