Complexity dynamics and simulations in a discrete switching ecosystem induced by an intermittent threshold control strategy

Xinli Hu; Wenjie Qin; Marco Tosato; Xinli Hu; Wenjie Qin; Marco Tosato

doi:10.3934/mbe.2020115

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 3: 2164-2178. doi: 10.3934/mbe.2020115

Previous Article Next Article

Research article

Complexity dynamics and simulations in a discrete switching ecosystem induced by an intermittent threshold control strategy

1.
School of Science, Xi’an Polytechnic University, Xi’an 710048, China
2.
Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China
3.
Laboratory for Industrial and Applied Mathematics, York University, Toronto, M3J 1P3, Canada

Received: 31 October 2019 Accepted: 05 January 2020 Published: 10 January 2020

Pest control is a worldwide challenge. An approach that has been developed to meet this challenge is the integrated pest management (IPM) strategy, which aims to offer environmentally sensitive solutions to pest problems, and takes into account the complex dynamics involved in the design of controlling pests. In this paper, we propose a discrete switching host-parasitoid model with a threshold control strategy, meanwhile, provide some qualitative analyses of the complexity of dynamic behaviors of the model that includes single and multi-parameter bifurcations and chaos. Furthermore, we do some numerical bifurcations and parameter sensibility analysis, revealing how the key control parameters and initial interaction state between the two populations affect pest control, as well as the dynamical balance between of the hosts and parasitoids. The model and analytical techniques developed in this work could be applied in other settings relevant to threshold control strategies.
- switching model,
- pest control,
- threshold policy,
- multiple coexisting attractors,
- dynamic complexity
Citation: Xinli Hu, Wenjie Qin, Marco Tosato. Complexity dynamics and simulations in a discrete switching ecosystem induced by an intermittent threshold control strategy[J]. Mathematical Biosciences and Engineering, 2020, 17(3): 2164-2178. doi: 10.3934/mbe.2020115

Related Papers:

Abstract

Pest control is a worldwide challenge. An approach that has been developed to meet this challenge is the integrated pest management (IPM) strategy, which aims to offer environmentally sensitive solutions to pest problems, and takes into account the complex dynamics involved in the design of controlling pests. In this paper, we propose a discrete switching host-parasitoid model with a threshold control strategy, meanwhile, provide some qualitative analyses of the complexity of dynamic behaviors of the model that includes single and multi-parameter bifurcations and chaos. Furthermore, we do some numerical bifurcations and parameter sensibility analysis, revealing how the key control parameters and initial interaction state between the two populations affect pest control, as well as the dynamical balance between of the hosts and parasitoids. The model and analytical techniques developed in this work could be applied in other settings relevant to threshold control strategies.

References

[1]	J. C. Van Lenteren, J. Woets, Biological and integrated pest control in greenhouses, Annu. Rev. Entomol., 33 (1998), 239-269.
[2]	S. E. Kunz, K. D. Murrell, G. Lambert, L. F. James, C. E. Terrill, Estimated losses of livestock to pests, in Handbook of Pest Management in Agriculture, Boca Raton, CRC Press, 1 (1991), 69-98.
[3]	R. L. Metcalf, W. H. Luckmann, Introduction to Insect Pest Management, 3nd edition, John Wiley Sons INC, New York, 1994.
[4]	T. W. Culliney, Crop losses to arthropods, in Integrated Pest Management: Pesticide Problems, (eds. D. Pimentel and P. Peshin), Dordrecht: Springer, (2014), 201-225.
[5]	A. Fournier-Level, The future of pest control lies within (the pest), Australas. Sci., 38 (2017), 23-24.
[6]	D. Pimentel, World Food, Pest Losses, and the Environment, CRC Press, Boca Raton, 2019.
[7]	Revolution from the Ground up Securing World Food Supplies with Integrated Crop Protection. Available from: https://www.research.bayer.com/en/revolution-from-the-ground-up.aspx.
[8]	C. Augusto, M. L. Juarez, M. G. Socias, M. G. Mura, S. Prieto, S. Medina, et al., Review of the host plants of fall armyworm, spodoptera frugiperda (lepidoptera: Noctuidae), Rev. Soc. Entomol. Argent., 69 (2010), 209-231.
[9]	J. L. Apple, R. F. Smith, Integrated Pest Management, Springer-Verlag, New York, 1976.
[10]	J. C. Van Lenteren, Integrated pest management in protected crops, in Integrated Pest Management Chapman, Hall, (1995), 311-320.
[11]	M. A. Altieri, J. G. Farrell, S. B. Hecht, M. Liebman, F. Magdoff, B. Murphy, et al., Integrated pest management, in Agroecology, CRC Press, (2018), 267-281.
[12]	G. J. Hallman, D. L. Denlinger, Temperature sensitivity in insects and application, in Integrated Pest Management, CRC Press, 2019.
[13]	J. A. McMurtry, N. F. Sourassou, P. R. Demite, The phytoseiidae (acari: Mesostigmata) as biological control agents, in Prospects for Biological Control of Plant Feeding Mites and Other Harmful Organisms, Springer, Cham, (2015), 133-149.
[14]	G. R. Stirling, Biological control of plant-parasitic nematodes, in Diseases of Nematodes, CRC Press, (2018), 103-150.
[15]	G. O. Poinar, Nematodes for Biological Control of Insects, CRC press, 2018.
[16]	G. M. Gurr, H. F. Van Emden, S. D. Wratten, Habitat manipulation and natural enemy efficiency: Implications for the control of pests, in Conservation Biological Control, Academic Press, (1988), 155-183.
[17]	D. Pimentel, Pesticides and pest control, in Integrated Pest Management: InnovationDevelopment Process, Springer, (2009), 83-87.
[18]	S. Tang, Y. Xiao, R. A. Cheke, Dynamical analysis of plant disease models with cultural control strategies and economic thresholds, Math. Comput. Simul., 80 (2010), 894-921.
[19]	K. R. Summy, E. G. King, Cultural control of cotton insect pests in the United States, Crop Prot., 11 (1992), 307-319.
[20]	E. C. Oerke, Crop losses to pests, J. Agric. Sci., 144 (2006), 31-43.
[21]	V. I. Utkin, Sliding Modes and Their Applications in Variable Structure Systems, Mir Publishers. 1978.
[22]	V. I. Utkin, Sliding Modes in Control and Optimization, Springer-Verlag, 1992.
[23]	L. P. Pedigo, S. H. Hutchins, L. G. Higley, Economic injury levels in theory and practice, Annu. Rev. Entomol., 31 (1986), 341-368.
[24]	J. C. Headley, Defining the economic threshold, in Pest Control Strategies for the Future, 1972.
[25]	H. C. Chiang, General model of the economic threshold level of pest populations, in Plant Protection Bulletin, 1979.
[26]	S. Tang, R. A. Cheke, State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences, J. Math. Biol., 50 (2005), 257-292.
[27]	S. Tang, J. Liang, Y. Xiao, R. A. Cheke, Sliding bifurcations of Filippov two stage pest control models with economic thresholds, SIAM J. Appl. Math., 72 (2012), 1061-1080.
[28]	S. Tang, C. Li, B. Tang, X. Wang, Global dynamics of a nonlinear state-dependent feedback control ecological model with a multiple-hump discrete map, Commun. Nonlinear Sci. Numer. Simul., 79 (2019), 104900.
[29]	W. Qin, X. Tan, X. Shi, J. Chen, Dynamics and bifurcation analysis of a Filippov predator-prey ecosystem in a seasonally fluctuating environment, Int. J. Bifurcation Chaos, 29 (2019), 1950020.
[30]	W. Qin, X. Tan, M. Tosato, X. Liu, Threshold control strategy for a non-smooth Filippov ecosystem with group defense, Appl. Math. Comput., 362 (2019), 124532.
[31]	R. J. Beverton, S. J. Holt, The Theory of Fishing, Sea Fisheries; Their Investigation in the United Kingdom, Edward Arnold, London, 1956.
[32]	J. M. Cushing, S. M. Henson, A periodically forced Beverton-Holt equation, J. Differ. Eq. Appl., 8 (2002), 1119-1120.
[33]	V. L. Kocic, G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Dordrecht Kluwer Academic Publishers, 1993.
[34]	A. J. Nicholson, V. A. Bailey, The balance of animal populations, in Part I. Proceedings of the Zoological Society of London, (1935), 551-598.
[35]	S. Tang, Y. Xiao, R. A. Cheke, Multiple attractors of host-parasitoid models with integrated pest management strategies: Eradication, persistence and outbreak, Theor. Popul. Biol., 73 (2008), 181-197.
[36]	E. I. Jury, Inners and Stability of Dynamic Systems, Wiley, New York, 1974.
[37]	C. Xiang, Z. Xiang, S. Tang, J. Wu, Discrete switching host-parasitoid models with integrated pest control, Int. J. Bifurcation Chaos, 24 (2014), 1450114.
[38]	L. Zhang, C. Zhang, Dynamics of a hyperparasitic system with prolonged diapause for host, Int. J. Mod. Nonlinear Theory Appl., 2 (2013), 201-208.
[39]	P. Wang, W. Qin, G. Tang, Modelling and analysis of a Host-Parasitoid impulsive ecosystem under resource limitation, Complexity, 2019 (2019), 9365293.
[40]	J. Liang, S. Tang, R. A. Cheke, Beverton-Holt discrete pest management models with pulsed chemical control and evolution of pesticide resistance, Commun. Nonlinear Sci. Numer. Simul., 36 (2016), 327-341.
[41]	W. Qin, X. Tan, X. Shi, C. Xiang, IPM strategies to a discrete switching predator-prey model induced by a mate-finding Allee effect, J. Biol. Dyn., 13 (2019), 586-605.

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)