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Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance

Author

Listed:
  • Xiaoxiao Liu

    (College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China)

  • Chunrui Zhang

    (College of Science, Northeast Forestry University, Harbin 150040, China)

Abstract

In this article, we propose a mathematical model for insect outbreaks coupled with wildfire disturbances and an optimization model for finding suitable wildfire frequencies. We use a refined Holling II function as a model for the nonlinear response of fire frequency against trees and insects. The results show that for the tree–insect–wildfire model, there is a coexistence equilibrium in the system. Sensitivity analysis is performed to determine the effect of wildfire on trees in the optimization model. The results show that forest fires have a significant impact on the equilibrium mechanism of tree–insect coexistence. Numerical simulations suggest that in some areas of high fire intensity, there may be positive feedback between disturbances from wildfires and insect outbreaks. The result is consistent with the present theory in this field.

Suggested Citation

  • Xiaoxiao Liu & Chunrui Zhang, 2022. "Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance," Mathematics, MDPI, vol. 10(15), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2563-:d:869559
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    References listed on IDEAS

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    1. Chen-Charpentier, B. & Leite, M.C.A., 2014. "A model for coupling fire and insect outbreak in forests," Ecological Modelling, Elsevier, vol. 286(C), pages 26-36.
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    Cited by:

    1. Binhao Hong & Chunrui Zhang, 2023. "Neimark–Sacker Bifurcation of a Discrete-Time Predator–Prey Model with Prey Refuge Effect," Mathematics, MDPI, vol. 11(6), pages 1-13, March.

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