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

Lijun Zhang | Zendy; Jianming Zhang | Zendy

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

Author(s) -

Lijun Zhang,

Jianming Zhang

Publication year - 2020

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/20200084

Subject(s) - hopf bifurcation , center manifold , mathematics , pitchfork bifurcation , transcritical bifurcation , saddle node bifurcation , bifurcation diagram , bogdanov–takens bifurcation , stability (learning theory) , mathematical analysis , bifurcation , physics , nonlinear system , computer science , quantum mechanics , machine learning

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.

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