Hopf Bifurcation Analysis of a Model for Spruce Budworm Populations With Delays

CAO Jianzhi; TAN Jun; WANG Peiguang

doi:10.21656/1000-0887.390111

Volume 40 Issue 3

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CAO Jianzhi, TAN Jun, WANG Peiguang. Hopf Bifurcation Analysis of a Model for Spruce Budworm Populations With Delays[J]. Applied Mathematics and Mechanics, 2019, 40(3): 332-342. doi: 10.21656/1000-0887.390111

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Hopf Bifurcation Analysis of a Model for Spruce Budworm Populations With Delays

doi: 10.21656/1000-0887.390111

Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province; College of Mathematics and Information Science, Hebei University, Baoding, Hebei 071002, P.R.China

Funds: The National Natural Science Foundation of China(11771115)

Received Date: 2018-04-08
Rev Recd Date: 2018-12-18
Publish Date: 2019-03-01

Abstract

Abstract

The dynamic behavior of a population model with stage structure for spruce budworms with time delay was investigated. Firstly, existence of a unique positive equilibrium of the model was discussed and sufficient conditions for local stability of the positive equilibrium and Hopf bifurcation occurrence were obtained. Next, the direction of the Hopf bifurcation and the stability of the periodic bifurcation solutions were analyzed with the normal form method combined with the center manifold theorem. Finally, some numerical simulations to verify the theoretical results were also conducted. The work provides an applicable reference for control of spruce budworms.
- spruce budworm population model,
- equilibrium,
- stability,
- Hopf bifurcation

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References(17)

References

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