Abstract
Dynamical analysis of a delayed tri-trophic food chain consisting of prey, an intermediate, and a top predator is investigated in this paper. The additive Allee effect is introduced in the prey population, and it is assumed that there is a time lag due to the gestation effect in the intermediate predator. The interference among the prey and the intermediate predator is according to Holling type II, while the interaction between the intermediate and top predators follows the Crowley–Martin functional response. The local stability and bifurcation analysis of the proposed model at the interior equilibrium point are studied. Numerical simulations are provided to ensure the mathematical results.
Highlights
In ecology, the interaction between various species is a common natural phenomenon, which can be described with mathematical models
6 Conclusion In this paper, we have considered the dynamics of the food chain model by incorporating the effect of gestation delay in the intermediate predator and the Allee effect in prey
The existence of equilibrium points and their local dynamics were discussed for the non-delayed model
Summary
The interaction between various species is a common natural phenomenon, which can be described with mathematical models. Zhang et al [43] studied the local stability and Hopf bifurcation analysis in a singular bio-economic model with Allee effect and two-time delays. They examined the stable region in two delay parameter spaces. To the authors’ best knowledge, it is evident that the additive Allee effect in the prey population has yet to be introduced in the food chain model with time delays in [44], which has inspired our present study. The intrinsic growth rate of the prey species is affected by the additive type Allee effect in the food chain model [44]. To reduce the complexity of the considered model, consider the following nondimensional scheme: X
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