IMPULSIVE CONTROL FOR A PLANT-PEST-NATURAL ENEMY MODEL WITH STAGE STRUCTURE

Weixuan Shi; Sha Lu; Jianzhong Zhang

doi:10.11948/20240083

2025 Volume 15 Issue 1

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(1): 261-285

Next Article Previous Article

Weixuan Shi, Sha Lu, Jianzhong Zhang. IMPULSIVE CONTROL FOR A PLANT-PEST-NATURAL ENEMY MODEL WITH STAGE STRUCTURE[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 261-285. doi: 10.11948/20240083

Citation:

Weixuan Shi, Sha Lu, Jianzhong Zhang. IMPULSIVE CONTROL FOR A PLANT-PEST-NATURAL ENEMY MODEL WITH STAGE STRUCTURE[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 261-285. doi: 10.11948/20240083

IMPULSIVE CONTROL FOR A PLANT-PEST-NATURAL ENEMY MODEL WITH STAGE STRUCTURE

1.
School of Science, Jiangnan University, Wuxi 214122, China
2.
Colleqe of Qeneral Aviation and Fliqht, Nanjing University of Aeronautics and Astronautics, Changzhou 213300, China
3.
School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China

Author Bio: Email: wxshi_0610@jiangnan.edu.cn(W. Shi); Email: zhangjz_91@sdtbu.edu.cn(J. Zhang)
Corresponding author: Email: lusha0828@nuaa.edu.cn(S. Lu)
Fund Project: The first author was supported by the China Postdoctoral Science Foundation (2023M731341). The second author was supported by the Fundamental Research Funds for the Central Universities (1027-YAT22021)

Abstract

Abstract

For integrated pest management (IPM), we propose a generalized stage-structured plant-pest-natural enemy system with impulsive spraying pesticide and releasing natural enemies at different fixed moment. By the stroboscopic maps, we obtain two types of periodic solutions: the plant-pest-extinction and the pest-extinction. The sufficient conditions for the global attractivity of a pest-extinction periodic solution and permanence of the system are obtained by comparison theorem and stroboscopic technique. Moreover, numerical simulations are inserted to verify the effectiveness and feasibility of the theoretical results, which show that the impulsive control plays a key role on the permanence of the system.
- Impulsive control /
- stage-structure /
- global attractivity /
- permanence
MSC: 34A37, 34D45, 92D45

FullText(HTML)

References

[1]	O. Akmana, T. Comar and M. Hendersona, An analysis of an impulsive stage structured integrated pest management model with refuge effect, Chaos, Soliton. & Fract., 2018, 111, 44–54. doi: 10.1016/j.chaos.2018.03.039 CrossRef Google Scholar
[2]	D. D. Bainov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific and Technical, New York, 1993. Google Scholar
[3]	Q. J. Chen, Z. J. Liu, Y. S. Tan, et al., Analysis of a stochastic hybrid population model with impulsive perturbations and allee effect, J. Appl. Math. Comput., 2023, 69(1), 565–587. doi: 10.1007/s12190-022-01752-9 CrossRef Google Scholar
[4]	Y. P. Chen, Z. J. Liu and M. Haque, Analysis of a leslie-gower-type prey-predator model with periodic impulsive perturbations, Commun. Nonlinear Sci., 2009, 14(8), 3412–3423. doi: 10.1016/j.cnsns.2008.12.019 CrossRef Google Scholar
[5]	P. Cull, Global stability of population models, B. Math. Biol., 1981, 43(1), 47–58. doi: 10.1016/S0092-8240(81)80005-5 CrossRef Google Scholar
[6]	B. Dubey and A. Kumar, Dynamics of prey-predator model with stage structure in prey including maturation and gestation delays, Nonlinear Dynam., 2019, 96(4), 2653–2679. doi: 10.1007/s11071-019-04951-5 CrossRef Google Scholar
[7]	P. Georgescu and G. Morosanu, Impulsive perturbations of a three-trophic prey-dependent food chain system, Math. Comput. Model., 2008, 48(7), 975–997. Google Scholar
[8]	M. P. Hoffmann and A. C. Frodsham, Natural Enemies of Vegetable Insect Pests, Cooperative Extension, Cornell University, Ithaca, New York, 1993. Google Scholar
[9]	G. X. Hu and K. H. Tian, On hybrid stochastic population models with impulsive perturbations, J. Biol. Dynam., 2019, 13(1), 385–406. doi: 10.1080/17513758.2019.1609607 CrossRef Google Scholar
[10]	S. C. Hu, V. Lakshmikantham and S. Leela, Impulsive differential systems and the pulse phenomena, J. Math. Anal. Appl., 1989, 137(2), 605–612. doi: 10.1016/0022-247X(89)90266-7 CrossRef Google Scholar
[11]	H. F. Huo, F. H. Zhang and H. Xiang, Spatiotemporal dynamics for impulsive eco-epidemiological model with crowley-martin type functional response, Math. Biosci. Eng., 2022, 19(12), 12180–12211. doi: 10.3934/mbe.2022567 CrossRef Google Scholar
[12]	K. S. Jatav and J. Dhar, Hybrid approach for pest control with impulsive releasing of natural enemies and chemical pesticides: A plant-pest-natural enemy model, Nonlinear Anal.-Hybri., 2014, 12, 79–92. doi: 10.1016/j.nahs.2013.11.011 CrossRef Google Scholar
[13]	V. Kumar, J. Dhar and H. S. Bhatti, Stage-structured plant-pest-natural enemy interaction dynamics incorporating gestation delay for both pest and natural enemy, Model. Earth Syst. Env., 2019, 5(1), 59–69. doi: 10.1007/s40808-018-0518-x CrossRef Google Scholar
[14]	V. Kumari, S. Chauhan and J. Dhar, Controlling pest by integrated pest management: A dynamical approach, Int. J. Math. Eng. Manag., 2020, 5(4), 769–786. Google Scholar
[15]	V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapor, 1989. Google Scholar
[16]	W. J. Li, J. C. Ji and L. H. Huang, Global dynamic behavior of a predator-prey model under ratio-dependent state impulsive control, Appl. Math. Model., 2020, 77, 1842–1859. doi: 10.1016/j.apm.2019.09.033 CrossRef Google Scholar
[17]	W. X. Li and K. Wang, Optimal harvesting policy for general stochastic logistic population model, J. Math. Anal. Appl., 2010, 368(2), 420–428. doi: 10.1016/j.jmaa.2010.04.002 CrossRef Google Scholar
[18]	J. Liu, J. Hu and P. Yuen, Extinction and permanence of the predator-prey system with general functional response and impulsive control, Appl. Math. Model., 2020, 88, 55–67. doi: 10.1016/j.apm.2020.06.033 CrossRef Google Scholar
[19]	Y. J. Niu, D. Liao and P. Wang, Stochastic asymptotical stability for stochastic impulsive differential equations and it is application to chaos synchronization, Commun. Nonlinear Sci., 2012, 17(2), 505–512. doi: 10.1016/j.cnsns.2011.07.011 CrossRef Google Scholar
[20]	Y. Z. Pei, Y. Yang and C. G. Li, Dynamics of an impulsive control system which prey species share a common predator, Chaos, Soliton. & Fract., 2009, 41(5), 2429–2436. Google Scholar
[21]	X. Y. Song, M. Y. Hao and X. Z. Meng, A stage-structured predator-prey model with disturbing pulse and time delays, Appl. Math. Model., 2009, 33(1), 211–223. doi: 10.1016/j.apm.2007.10.020 CrossRef Google Scholar
[22]	J. A. Souza and L. H. Takamoto, Lyapunov stability for impulsive control affine systems, J. Differ. Equations, 2019, 266(7), 4232–4267. doi: 10.1016/j.jde.2018.09.033 CrossRef Google Scholar
[23]	J. T. Sun, H. B. Chen and L. Yang, Variational methods to fourth-order impulsive differential equations, J. Appl. Math. Comput., 2011, 35(1), 323–340. Google Scholar
[24]	S. Y. Tang, Y. N. Xiao, L. S. Chen, et al., Integrated pest management models and their dynamical behaviour, B. Math. Biol., 2005, 67(1), 115–135. doi: 10.1016/j.bulm.2004.06.005 CrossRef Google Scholar
[25]	L. S. Wang, R. Xu and G. H. Feng, A stage-structured predator-prey system with impulsive effect and holling type-Ⅱ functional response, Journal of Mathematical Research and Exposition, 2011, 31(1), 147–156. Google Scholar
[26]	H. G. Yu, S. M. Zhong, M. Ye, et al., Mathematics and dynamic analysis of an ecological model with impulsive control strategy and distributed time delay, Math. Comput. Model., 2009, 50(11), 1622–1635. Google Scholar
[27]	B. Zeng and Z. H. Liu, Existence results for impulsive feedback control systems, Nonlinear Anal.-Hybri., 2019, 33, 1–16. doi: 10.1016/j.nahs.2019.01.008 CrossRef Google Scholar
[28]	Q. Q. Zhang, S. Y. Tang and X. F. Zou, Rich dynamics of a predator-prey system with state-dependent impulsive controls switching between two means, J. Differ. Equations, 2023, 364, 336–377. doi: 10.1016/j.jde.2023.03.030 CrossRef Google Scholar
[29]	S. W. Zhang and D. J. Tan, Dynamics of a stochastic predator-prey system in a polluted environment with pulse toxicant input and impulsive perturbations, Appl. Math. Model., 2015, 39(20), 6319–6331. doi: 10.1016/j.apm.2014.12.020 CrossRef Google Scholar