Optimal predator control policy and weak Allee effect in a delayed prey–predator system

Biswas, Sambhunath

doi:10.1007/s11071-017-3854-x

Cited by 9 publications

(2 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Again, on the issue of population control, we usually get very useful suggestions from mathematical modeling of the concerned system. Very often, modelers identify the factors which might leave a stabilizing or destabilizing influence on the underlying system [8,15]. In our model, we have observed some patterns like spiral pattern, cyclic pattern, etc.…”

Section: Discussionmentioning

confidence: 75%

A competition model with herd behaviour and allee effect

Sen

Maiti²,

Samanta

2019

Filomat

View full text Add to dashboard Cite

In this work we have studied the deterministic behaviours of a competition model with herd behaviour and Allee effect. The uniform boundedness of the system has been studied. Criteria for local stability at equilibrium points are derived. The effect of discrete time-delay on the model is investigated. We have carried out numerical simulations to validate the analytical findings. The biological implications of our analytical and numerical findings are discussed.

show abstract

Section: Discussionmentioning

confidence: 75%

A competition model with herd behaviour and allee effect

Sen

Maiti²,

Samanta

2019

Filomat

View full text Add to dashboard Cite

show abstract

“…Some studies have been conducted with Allee effect including gestation delay [4,5,29,31]. Li et al [23] investigated the stability and Hopf-bifurcation of a delayed density dependent prey-predator system with Beddington-DeAngelis functional response.…”

Section: Introductionmentioning

confidence: 99%

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

Kumar

Dubey

2020

NAMC

View full text Add to dashboard Cite

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.

show abstract