Bifurcation analysis of a delayed predator-prey system with strong Allee effect and diffusion. (English) Zbl 1266.34135
This paper deals with a predator-prey model including two constant delays in the interspecies interaction terms of both populations and an Allee effect in preys.
Firstly, the stability of a positive equilibrium is analyzed, establishing the existence of a Hopf bifurcation for some critical values of the delays. Using standard methods from the \(\mathrm{C}_0\)-semigroup theory, the direction of the bifurcation and the stability of the nontrivial periodic solution are given.
Secondly, a modification of the model including a diffusion term for a one-dimensional spatial variable, with Neumann boundary conditions is analyzed.
The paper illustrates the theoretical results by including some numerical simulations for both versions of the model.
Firstly, the stability of a positive equilibrium is analyzed, establishing the existence of a Hopf bifurcation for some critical values of the delays. Using standard methods from the \(\mathrm{C}_0\)-semigroup theory, the direction of the bifurcation and the stability of the nontrivial periodic solution are given.
Secondly, a modification of the model including a diffusion term for a one-dimensional spatial variable, with Neumann boundary conditions is analyzed.
The paper illustrates the theoretical results by including some numerical simulations for both versions of the model.
Reviewer: Eva Sánchez (Madrid)
MSC:
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 92D25 | Population dynamics (general) |
| 34K18 | Bifurcation theory of functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 35K57 | Reaction-diffusion equations |
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