Dynamic Analysis of Delayed Two-Species Interaction Model with Age Structure: An Application to Larch-Betula Platyphylla Forests in the Daxing’an Mountains, Northeast China

Xuan Huang, Yuting Ding () and Ning Pan
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Xuan Huang: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Yuting Ding: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Ning Pan: Department of Mathematics, Northeast Forestry University, Harbin 150040, China

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

Abstract: Since plant–plant interaction has been the fundamental issue of the ecology community and is essential for the multispecies forest community, it is necessary to analyze the interaction mechanisms and provide suggestions for collaborative management of multispecies forests with the background of double carbon goals in China. To explore the interaction mechanisms in different interaction modes and assist China’s green development, we choose the most promising area, the Daxing’an Mountains, and its dominant species, Larch and Betula platyphylla, as research objects and establish a delayed two-species interaction model with an age structure. First, we calculate the equilibria of our model and analyze the stability of equilibria. Then, we study the existence of the Hopf bifurcation near the equilibria. Furthermore, we determine reasonable parameter values based on official data through mathematical methods, such as cluster analysis and model fitting. Finally, we carry out numerical simulations from three aspects, the evolution of a stand structure without interactions, the population dynamics in different interaction modes, and the influences of the parameters on the equilibria. Combined with simulation results, we provide biological interpretations for simulations of the stand structure evolution process and the interactions between Larch and Betula platyphylla; we also give reasonable values of the growth rates and mortalities for developing forest strategies.

Keywords: two-species interaction model; larch and betula platyphylla; age structure; time delay; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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