IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v266y2015icp95-107.html

Periodic solution of a prey–predator model with nonlinear state feedback control

Author

Listed:
  • Zhang, Tongqian
  • Ma, Wanbiao
  • Meng, Xinzhu
  • Zhang, Tonghua

Abstract

Assume that when the number of pests reaches the certain threshold, pest management strategy will be taken to control pests. Based on this assumption, in this paper, we propose a pest management model with nonlinear state feedback control. We then analyze the dynamic behavior of the model. More precisely, we first investigate the singularity of the model by using method of qualitative analysis; secondly the existence of periodic solution of the model is studied by using successor functions and Poincaré–Bendixson theorem; and then it is followed by the study of the stability of periodic solution; finally, an example with numerical simulations is given to illustrate our conclusions.

Suggested Citation

  • Zhang, Tongqian & Ma, Wanbiao & Meng, Xinzhu & Zhang, Tonghua, 2015. "Periodic solution of a prey–predator model with nonlinear state feedback control," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 95-107.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:95-107
    DOI: 10.1016/j.amc.2015.05.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315006323
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.05.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. D. Hueth & U. Regev, 1974. "Optimal Agricultural Pest Management with Increasing Pest Resistance," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 56(3), pages 543-552.
    2. Hui, Jing & Zhu, Deming, 2006. "Dynamic complexities for prey-dependent consumption integrated pest management models with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 233-251.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Meng, Xinzhu & Li, Fei & Gao, Shujing, 2018. "Global analysis and numerical simulations of a novel stochastic eco-epidemiological model with time delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 701-726.
    2. Feifei Bian & Wencai Zhao & Yi Song & Rong Yue, 2017. "Dynamical Analysis of a Class of Prey-Predator Model with Beddington-DeAngelis Functional Response, Stochastic Perturbation, and Impulsive Toxicant Input," Complexity, Hindawi, vol. 2017, pages 1-18, December.
    3. Bor-Sen Chen & Xiangyun Lin & Weihai Zhang & Tianshou Zhou, 2018. "On the System Entropy and Energy Dissipativity of Stochastic Systems and Their Application in Biological Systems," Complexity, Hindawi, vol. 2018, pages 1-18, December.
    4. Saifuddin, Md. & Biswas, Santanu & Samanta, Sudip & Sarkar, Susmita & Chattopadhyay, Joydev, 2016. "Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 270-285.
    5. Ihsan Ullah Khan & Sanyi Tang & Biao Tang, 2019. "The State-Dependent Impulsive Model with Action Threshold Depending on the Pest Density and Its Changing Rate," Complexity, Hindawi, vol. 2019, pages 1-15, June.
    6. Liu, Xia & Zhang, Tonghua & Meng, Xinzhu & Zhang, Tongqian, 2018. "Turing–Hopf bifurcations in a predator–prey model with herd behavior, quadratic mortality and prey-taxis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 446-460.
    7. Peng, Yahong & Zhang, Tonghua, 2016. "Turing instability and pattern induced by cross-diffusion in a predator-prey system with Allee effect," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 1-12.
    8. Li, Qian & Liu, Xinzhi & Zhu, Qingxin & Zhong, Shouming & Zhang, Dian, 2019. "Distributed state estimation for stochastic discrete-time sensor networks with redundant channels," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 230-246.
    9. Tingting Ma & Xinzhu Meng & Zhengbo Chang, 2019. "Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps," Complexity, Hindawi, vol. 2019, pages 1-19, March.
    10. Liu, Fuxiang & Yang, Ruizhi & Tang, Leiyu, 2019. "Hopf bifurcation in a diffusive predator-prey model with competitive interference," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 250-258.
    11. Tian, Yuan & Li, Chunxue & Liu, Jing, 2023. "Complex dynamics and optimal harvesting strategy of competitive harvesting models with interval-valued imprecise parameters," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    12. Shan, Yaonan & She, Kun & Zhong, Shouming & Zhong, Qishui & Shi, Kaibo & Zhao, Can, 2018. "Exponential stability and extended dissipativity criteria for generalized discrete-time neural networks with additive time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 145-168.
    13. Tian, Yuan & Gao, Yan & Sun, Kaibiao, 2022. "Global dynamics analysis of instantaneous harvest fishery model guided by weighted escapement strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    14. Sun, Kaibiao & Zhang, Tonghua & Tian, Yuan, 2017. "Dynamics analysis and control optimization of a pest management predator–prey model with an integrated control strategy," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 253-271.
    15. Li, Hongjie & Zhu, Yinglian & jing, Liu & ying, Wang, 2018. "Consensus of second-order delayed nonlinear multi-agent systems via node-based distributed adaptive completely intermittent protocols," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 1-15.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gardner Brown & Ramanan Laxminarayan, 1998. "Economics of Antibiotic Resistance," Working Papers 0060, University of Washington, Department of Economics.
    2. Lichtenberg, Erik & Zilberman, David & Archibald, Sandra O., 1990. "Economics and Pesticides," Working Papers 197750, University of Maryland, Department of Agricultural and Resource Economics.
    3. Yerokhin, Oleg & Moschini, GianCarlo, 2007. "Intellectual Property Rights and Crop-Improving R&D under Adaptive Destruction," Hebrew University of Jerusalem Archive 10008, Hebrew University of Jerusalem.
    4. repec:isu:genstf:2000010108000013359 is not listed on IDEAS
    5. Marsh, Sally P. & Llewellyn, Rick S. & Powles, Stephen B., 2006. "Social costs of herbicide resistance: the case of resistance to glyphosate," 2006 Conference (50th), February 8-10, 2006, Sydney, Australia 139881, Australian Agricultural and Resource Economics Society.
    6. Just, Richard E. & Zilberman, David, 1985. "Income Distributional Implications Of Water Policy Decisions," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 10(2), pages 1-13, December.
    7. Christine L. Carroll & Colin A. Carter & Rachael E. Goodhue & C.-Y. Cynthia Lin Lawell, 2017. "Crop Disease and Agricultural Productivity," NBER Working Papers 23513, National Bureau of Economic Research, Inc.
    8. Marsh, Thomas L. & Huffaker, Ray G. & Folwell, Raymond J. & Long, Gary, 1998. "An Intraseasonal Bioeconomic Model Of Plrv Net Necrosis," 1998 Annual meeting, August 2-5, Salt Lake City, UT 20935, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    9. Laxminarayan, Ramanan & Brown, Gardner M., Jr., 2000. "Economics of Antibiotic Resistance: A Theory of Optimal Use," Discussion Papers 10619, Resources for the Future.
    10. Carter, Colin A. & Chalfant, James A. & Goodhue, Rachael E., 2004. "Invasive Species In Agriculture: A Rising Concern," Western Economics Forum, Western Agricultural Economics Association, vol. 3(2), pages 1-6, December.
    11. Liang, Xiyin & Pei, Yongzhen & Zhu, Meixia & Lv, Yunfei, 2016. "Multiple kinds of optimal impulse control strategies on plant–pest–predator model with eco-epidemiology," Applied Mathematics and Computation, Elsevier, vol. 287, pages 1-11.
    12. Clement A. Tisdell, 1986. "Levels Of Pest Control And Uncertainty Of Benefits," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 30(2-3), pages 157-161, 08-12.
    13. Archibald, Sandra O. & McCorkle, Chester O. Jr & Howitt, Richard E., 1986. "A Dynamic Analysis Of Production Externalities : Pesticide Resistance In California Cotton," Working Papers 225802, University of California, Davis, Department of Agricultural and Resource Economics.
    14. Russell J. Gorddard & David J. Pannell & Greg Hertzler, 1995. "An Optimal Control Model For Integrated Weed Management Under Herbicide Resistance," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 39(1), pages 71-87, April.
    15. Laxminarayan, Ramanan & Brown, Gardner M., 2001. "Economics of Antibiotic Resistance: A Theory of Optimal Use," Journal of Environmental Economics and Management, Elsevier, vol. 42(2), pages 183-206, September.
    16. Hurley, Terrance M. & Babcock, Bruce A. & Hellmich, Richard L., 2001. "Bt Corn And Insect Resistance: An Economic Assessment Of Refuges," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 26(01), pages 1-19, July.
    17. Desquilbet, Marion & Hermann, Markus, 2012. "An assessment of bioeconomic modeling of pest resistance with new insights into dynamic refuge fields," TSE Working Papers 12-263, Toulouse School of Economics (TSE).
    18. Just, Richard E. & Netanyahu, Sinaia & Olson, Lars J., 2005. "Depletion of natural resources, technological uncertainty, and the adoption of technological substitutes," Resource and Energy Economics, Elsevier, vol. 27(2), pages 91-108, June.
    19. Bullock, David S. & D'Arcangelo, Filippo Maria & Desquilbet, Marion, 2018. "A discussion of the market and policy failures associated with the adoption of herbicide-tolerant crops," TSE Working Papers 18-959, Toulouse School of Economics (TSE), revised Aug 2019.
    20. Brown, Zachary S. & Cho, Chanheung & Roh, Hyeongyul & Gross, Kevin & Tregeagle, Daniel, 2023. "A Global Sensitivity Analysis of the Price of Pesticide Resistance," 2023 Annual Meeting, July 23-25, Washington D.C. 335859, Agricultural and Applied Economics Association.
    21. Gu, Xi & Marsh, Thomas L., "undated". "Pesticide Substitution Under Maximum Residue Limits: Application to Hops Production," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258572, Agricultural and Applied Economics Association.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:95-107. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.