Qualitative Analysis of a Modified Leslie-Gower Model with Addictive Allee Effect and Gestation Delay

2020 ◽  
Vol 9 (3) ◽  
pp. 461-476
Author(s):  
S. Vinoth ◽  
R. Sivasamy ◽  
K. Sathiyanathan
Keyword(s):  
Qualitative Analysis ◽  
Allee Effect ◽  
Gestation Delay

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

2020 ◽  
Vol 25 (3) ◽  
Author(s):  
Ankit Kumar ◽  
Balram Dubey
Keyword(s):  
Allee Effect ◽  
Threshold Value ◽  
Prey Population ◽  
Predator Population ◽  
Allee Effects ◽  
Normal Form Theory ◽  
Delayed Systems ◽  
Gestation Delay ◽  
The Status ◽  
Manifold Theory

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. 

Effect of Multiple Delays in an Eco-Epidemiological Model with Strong Allee Effect

2017 ◽  
Vol 27 (11) ◽  
pp. 1750167 ◽  
Author(s):  
Kakali Ghosh ◽  
Santanu Biswas ◽  
Sudip Samanta ◽  
Pankaj Kumar Tiwari ◽  
Ali Saleh Alshomrani ◽  
...  
Keyword(s):  
Time Delays ◽  
Allee Effect ◽  
Epidemiological Model ◽  
Multiple Delays ◽  
Uniform Persistence ◽  
Time Lags ◽  
Gestation Delay ◽  
Interior Equilibrium ◽  
Proposed Model ◽  
Strong Allee Effect

In the present article, we make an attempt to investigate the effect of two time delays, logistic delay and gestation delay, on an eco-epidemiological model. In the proposed model, strong Allee effect is considered in the growth term of the prey population. We incorporate two time lags and inspect elementary mathematical characteristic of the proposed model such as boundedness, uniform persistence, stability and Hopf-bifurcation for all possible combinations of both delays at the interior equilibrium point of the system. We observe that increase in gestation delay leads to chaotic solutions through the limit cycle. We also observe that the Allee effect play a major role in controlling the chaos. We execute several numerical simulations to illustrate the proposed mathematical model and our analytical findings.

Sign in / Sign up

Export Citation Format

Share Document