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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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xuan Huang & Yuting Ding & Ning Pan, 2023. "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," Mathematics, MDPI, vol. 11(11), pages 1-20, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2485-:d:1157984
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    References listed on IDEAS

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    2. Filotas, Elise & Grant, Martin & Parrott, Lael & Rikvold, Per Arne, 2010. "The effect of positive interactions on community structure in a multi-species metacommunity model along an environmental gradient," Ecological Modelling, Elsevier, vol. 221(6), pages 885-894.
    3. Ugo Bastolla & Miguel A. Fortuna & Alberto Pascual-García & Antonio Ferrera & Bartolo Luque & Jordi Bascompte, 2009. "The architecture of mutualistic networks minimizes competition and increases biodiversity," Nature, Nature, vol. 458(7241), pages 1018-1020, April.
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