Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance
Abstract
:1. Introduction
2. Deterministic Model for Tree–Beetle–Fire System
Existence and Stability of Equilibrium
- (1)
- If , boundary equilibrium of system (3) is local asymptotically stable.
- (2)
- If , boundary equilibrium of system (3) is unstable.
- (1)
- If , coexistence equilibrium of system (3) is local asymptotically stable.
- (2)
- If , coexistence equilibrium of system (3) is unstable.
3. Optimal Control Strategy
Sensitivity Analysis and Numerical Simulations
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | |||||
---|---|---|---|---|---|
Beijing | 0.764572 | 0.048204 | 158.611171 | 1657.993 | 828.9964 |
Tianjin | 0.445343 | 0.021843 | 203.882824 | 3658.925 | 1829.463 |
Hebei | 0.154946 | 0.023128 | 66.995922 | 3455.703 | 1727.852 |
Shanxi | 0.252996 | 0.036412 | 69.4821260 | 2194.957 | 1097.479 |
Inner Mongoria | 0.561737 | 0.045826 | 122.5812760 | 1744.046 | 872.0231 |
Liaoning | 0.337569 | 0.016873 | 200.0673550 | 4736.759 | 2368.379 |
Jilin | 0.38393 | 0.006038 | 635.8630730 | 13236.66 | 6618.332 |
Heilongjiang | 0.239552 | 0.008569 | 279.546910 | 9326.556 | 4663.278 |
Shandong | 0.524125 | 0.024039 | 218.031458 | 3324.691 | 1662.345 |
Henan | 0.258396 | 0.046559 | 55.498005 | 1716.561 | 858.2804 |
Year | 2004 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 |
---|---|---|---|---|---|---|---|---|---|---|---|
Shanxi | 0.18412 | 0.1013 | 0.3149 | 0.0499 | 0.6372 | 0.048 | 0.2145 | 0.076 | 0.0814 | 0.0272 | 0.0299 |
Inner Mongoria | 0.51265 | 1.5358 | 1.7764 | 0.9129 | 0.1741 | 0.4464 | 0.0826 | 0.595 | 0.3847 | 0.1622 | 2.4805 |
Liaoning | 0.04303 | 0.1249 | 0.1424 | 0.0404 | 0.0577 | 0.0374 | 0.0143 | 0.1045 | 0.1922 | 0.1706 | 0.0802 |
Jilin | 0.03272 | 0.0445 | 0.0351 | 0.0084 | 0.024 | 0.0178 | 0.0063 | 0.0134 | 0.0541 | 0.0123 | 0.045 |
Heilong jiang | 18.55472 | 1.8402 | 9.9819 | 1.3779 | 0.1741 | 0.1046 | 0.0106 | 0.0301 | 0.0787 | 0.064 | 0.0883 |
Hebei | 0.13467 | 0.033 | 0.0443 | 0.0221 | 0.2169 | 0.2112 | 0.0422 | 0.1168 | 0.0471 | 0.0573 | 0.1157 |
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Liu, X.; Zhang, C. Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance. Mathematics 2022, 10, 2563. https://doi.org/10.3390/math10152563
Liu X, Zhang C. Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance. Mathematics. 2022; 10(15):2563. https://doi.org/10.3390/math10152563
Chicago/Turabian StyleLiu, Xiaoxiao, and Chunrui Zhang. 2022. "Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance" Mathematics 10, no. 15: 2563. https://doi.org/10.3390/math10152563
APA StyleLiu, X., & Zhang, C. (2022). Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance. Mathematics, 10(15), 2563. https://doi.org/10.3390/math10152563