Hopf and Bogdanov-Takens bifurcations of a delayed Bazykin model. (English) Zbl 07840586
In this paper, the authors investigated the Hopf and Bogdanov-Takens bifurcations of a delayed Bazykin predator-prey model with predator intraspecific interactions and ratio-dependent functional response. And they established sufficient conditions for the existence of Hopf bifurcation. Meanwhile, they also discussed the Bogdanov-Takens bifurcation based on the corresponding normal form restricted to the associated two-dimensional center manifold. Finally, some numerical simulations are carried out to illustrate the theoretical criteria through s the distribution of eigenvalues, the bifurcation diagrams of Hopf and Bogdanov-Takens bifurcations and phase portraits. The obtained results showed that the dynamics of prey and predator are very sensitive to parameters and delay perturbations which can play a great role in controlling and regulating the number of biological populations.
Reviewer: Xiaosong Tang (Ji’an)
MSC:
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 92D25 | Population dynamics (general) |
| 34K21 | Stationary solutions of functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 34K13 | Periodic solutions to functional-differential equations |
| 34K17 | Transformation and reduction of functional-differential equations and systems, normal forms |
| 34K18 | Bifurcation theory of functional-differential equations |
| 34K16 | Heteroclinic and homoclinic orbits of functional-differential equations |
Software:
DDE-BIFTOOLReferences:
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