STABILITY AND HOPF BIFURCATION ANALYSIS ON A SPRUCE-BUDWORM MODEL WITH DELAY

Lijun Zhang; Jianming Zhang

doi:10.11948/20200084

2020 Volume 10 Issue 6

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Lijun Zhang, Jianming Zhang. STABILITY AND HOPF BIFURCATION ANALYSIS ON A SPRUCE-BUDWORM MODEL WITH DELAY[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2711-2721. doi: 10.11948/20200084

Citation:

Lijun Zhang, Jianming Zhang. STABILITY AND HOPF BIFURCATION ANALYSIS ON A SPRUCE-BUDWORM MODEL WITH DELAY[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2711-2721. doi: 10.11948/20200084

STABILITY AND HOPF BIFURCATION ANALYSIS ON A SPRUCE-BUDWORM MODEL WITH DELAY

Lijun Zhang¹,
Jianming Zhang^2, ,

1.
College of Mathematics and Systems Science, Shandong University of Science and Technology Qingdao, Shandong, 266590, China
2.
Department of Mathematics, School of Science, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, 310018, China

Corresponding author: Email: jmzhang@zstu.edu.cn(J. Zhang)

Abstract

Abstract

In this paper, the dynamics of a spruce-budworm model with delay is investigated. We show that there exists Hopf bifurcation at the positive equilibrium as the delay increases. Some sufficient conditions for the existence of Hopf bifurcation are obtained by investigating the associated characteristic equation. By using the theory of normal form and center manifold, explicit expression for determining the direction of Hopf bifurcations and the stability of bifurcating periodic solutions are presented.
- Spruce-budworm /
- Hopf bifurcation /
- normal form /
- center manifold
MSC: 34K18, 34K20, 34K25

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References

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