Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance
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 re...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/15/2563 |
| _version_ | 1797441515076714496 |
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| author | Xiaoxiao Liu Chunrui Zhang |
| author_facet | Xiaoxiao Liu Chunrui Zhang |
| author_sort | Xiaoxiao Liu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T12:24:11Z |
| format | Article |
| id | doaj.art-da152efe26414147b5557bf200a62563 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T12:24:11Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-da152efe26414147b5557bf200a625632023-11-30T22:37:16ZengMDPI AGMathematics2227-73902022-07-011015256310.3390/math10152563Stability and Optimal Control of Tree-Insect Model under Forest Fire DisturbanceXiaoxiao Liu0Chunrui Zhang1College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, ChinaCollege of Science, Northeast Forestry University, Harbin 150040, ChinaIn 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.https://www.mdpi.com/2227-7390/10/15/2563forest firetree–beetle systemstabilitysensitivity analysisoptimal control |
| spellingShingle | Xiaoxiao Liu Chunrui Zhang Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance Mathematics forest fire tree–beetle system stability sensitivity analysis optimal control |
| title | Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance |
| title_full | Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance |
| title_fullStr | Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance |
| title_full_unstemmed | Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance |
| title_short | Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance |
| title_sort | stability and optimal control of tree insect model under forest fire disturbance |
| topic | forest fire tree–beetle system stability sensitivity analysis optimal control |
| url | https://www.mdpi.com/2227-7390/10/15/2563 |
| work_keys_str_mv | AT xiaoxiaoliu stabilityandoptimalcontroloftreeinsectmodelunderforestfiredisturbance AT chunruizhang stabilityandoptimalcontroloftreeinsectmodelunderforestfiredisturbance |