Hopf Bifurcation Analysis of a Class of Saperda populnea Infectious Disease Model with Delay

Fuyu Cai and Yuting Ding ()
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Fuyu Cai: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Yuting Ding: Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Mathematics, 2023, vol. 11, issue 20, 1-14

Abstract: Under the background of double carbon, it is important to study forest pests and diseases to improve forest carbon sink. In this paper, we establish a delayed model associated with the larvae and adults of Saperda populnea , susceptible poplars, and infected poplars. First, we analyze the existence and stability of the equilibrium of the model. Second, we study the existence of Hopf bifurcation near the equilibrium and obtain the normal form of Hopf bifurcation by the multiple time scales method. Then, we analyze the direction and stability of Hopf bifurcating periodic solutions. Third, we analyze and conjecture some parameter values based on official data, and carry out numerical simulations to verify our results. Finally, we give some suggestions on the prevention and control of Saperda populnea .

Keywords: Saperda populnea; delayed differential equation; poplar; Hopf bifurcation; stability analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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