IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v147y2021ics0960077921002836.html
   My bibliography  Save this article

Diffusion driven finite time blow-up and pattern formation in a mutualistic preys-sexually reproductive predator system: A comparative study

Author

Listed:
  • Batabyal, Saikat
  • Jana, Debaldev
  • Upadhyay, Ranjit Kumar

Abstract

Species have the general tendency to sustain their own survival chance in the ecology. In this paper, we design different diffusive model systems in which two prey populations make mutualistic relationship in which they are getting benefited from each other with their usual growth rate and sexually reproductive generalist predator preys upon the prey according to their functional responses. In the absence of generalist predator, there is no sign of mutualism between two prey. Sometimes environment may turn favourable for the invasive species, causing the growth of their population to outbreak. Biological control is an adopted strategy to limit harmful populations. To establish a control strategy that decreases the harmful population to healthy levels as opposed to high and risky levels, five different diffusive models have been introduced associated to their functional responses which are either prey dependent (Holling type-III and IV) or predator dependent (Beddington–DeAngelis, Crowley–Martin and and Hassel–Varley). The blow up phenomenon at finite time in spatial cases have been discussed for all the model systems. For each model system, mathematical conditions are established under which species can blow up at finite time. Spatio-temporal dynamics and weakly nonlinear analysis have been thoroughly studied. Stability analysis of these model systems have been investigated and concentrated on discussing the Turing patterns. Theoretical analysis of the patterns formations has been described by using amplitude equations and the results are validated by numerical simulations. Mathematical computations of the structural models have been studied and explored their blow up phenomena under the effects of diffusion with the pattern formation of preys and predator populations in the spatiotemporal domain.The best chance of survival of the species upon diffusion has been discussed elaborately.

Suggested Citation

  • Batabyal, Saikat & Jana, Debaldev & Upadhyay, Ranjit Kumar, 2021. "Diffusion driven finite time blow-up and pattern formation in a mutualistic preys-sexually reproductive predator system: A comparative study," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921002836
    DOI: 10.1016/j.chaos.2021.110929
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921002836
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110929?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Baleanu, Dumitru & Restrepo, Joel E. & Suragan, Durvudkhan, 2021. "A class of time-fractional Dirac type operators," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Wang, Yi & Cao, Jinde & Sun, Gui-Quan & Li, Jing, 2014. "Effect of time delay on pattern dynamics in a spatial epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 137-148.
    3. Batabyal, Saikat & Jana, Debaldev & Lyu, Jingjing & Parshad, Rana D., 2020. "Explosive predator and mutualistic preys: A comparative study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    4. Pimentel, David & Zuniga, Rodolfo & Morrison, Doug, 2005. "Update on the environmental and economic costs associated with alien-invasive species in the United States," Ecological Economics, Elsevier, vol. 52(3), pages 273-288, February.
    5. Xue, Lin, 2012. "Pattern formation in a predator–prey model with spatial effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5987-5996.
    6. Wang, Weiming & Zhang, Lei & Wang, Hailing & Li, Zhenqing, 2010. "Pattern formation of a predator–prey system with Ivlev-type functional response," Ecological Modelling, Elsevier, vol. 221(2), pages 131-140.
    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. Zhang, Feifan & Sun, Jiamin & Tian, Wang, 2022. "Spatiotemporal pattern selection in a nontoxic-phytoplankton - toxic-phytoplankton - zooplankton model with toxin avoidance effects," Applied Mathematics and Computation, Elsevier, vol. 423(C).

    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. Ghorai, Santu & Chakraborty, Bhaskar & Bairagi, Nandadulal, 2021. "Preferential selection of zooplankton and emergence of spatiotemporal patterns in plankton population," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    2. Huang, Tousheng & Yu, Chengfeng & Zhang, Kui & Liu, Xingyu & Zhen, Jiulong & Wang, Lan, 2023. "Complex pattern dynamics and synchronization in a coupled spatiotemporal plankton system with zooplankton vertical migration," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    3. Ceddia, M.G. & Bardsley, N.O. & Goodwin, R. & Holloway, G.J. & Nocella, G. & Stasi, A., 2013. "A complex system perspective on the emergence and spread of infectious diseases: Integrating economic and ecological aspects," Ecological Economics, Elsevier, vol. 90(C), pages 124-131.
    4. Blackwood, Julie & Hastings, Alan & Costello, Christopher, 2010. "Cost-effective management of invasive species using linear-quadratic control," Ecological Economics, Elsevier, vol. 69(3), pages 519-527, January.
    5. Fernandez, Arran & Restrepo, Joel E. & Suragan, Durvudkhan, 2022. "On linear fractional differential equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    6. Don Driscoll & Adam Felton & Philip Gibbons & Annika Felton & Nicola Munro & David Lindenmayer, 2012. "Priorities in policy and management when existing biodiversity stressors interact with climate-change," Climatic Change, Springer, vol. 111(3), pages 533-557, April.
    7. Mann Manyombe, M.L. & Tsanou, B. & Mbang, J. & Bowong, S., 2017. "A metapopulation model for the population dynamics of anopheles mosquito," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 71-91.
    8. Sinden, John Alfred & Griffith, Garry, 2007. "Combining economic and ecological arguments to value the environmental gains from control of 35 weeds in Australia," Ecological Economics, Elsevier, vol. 61(2-3), pages 396-408, March.
    9. Cook, David C., 2008. "Benefit cost analysis of an import access request," Food Policy, Elsevier, vol. 33(3), pages 277-285, June.
    10. Holmberg, Robert J. & Tlusty, Michael F. & Futoma, Elizabeth & Kaufman, Les & Morris, James A. & Rhyne, Andrew L., 2015. "The 800-Pound Grouper in the Room: Asymptotic Body Size and Invasiveness of Marine Aquarium Fishes," Marine Policy, Elsevier, vol. 53(C), pages 7-12.
    11. Rai, Rajesh Kumar & Scarborough, Helen, 2012. "Estimating the public benefits of mitigating damages caused by invasive plant species in a subsistence economy," 2012 Conference (56th), February 7-10, 2012, Fremantle, Australia 124421, Australian Agricultural and Resource Economics Society.
    12. Charles Perrings, 2016. "Options for managing the infectious animal and plant disease risks of international trade," Food Security: The Science, Sociology and Economics of Food Production and Access to Food, Springer;The International Society for Plant Pathology, vol. 8(1), pages 27-35, February.
    13. Aldrich, Preston R. & El-Zabet, Jermeen & Hassan, Seerat & Briguglio, Joseph & Aliaj, Enela & Radcliffe, Maria & Mirza, Taha & Comar, Timothy & Nadolski, Jeremy & Huebner, Cynthia D., 2015. "Monte Carlo tests of small-world architecture for coarse-grained networks of the United States railroad and highway transportation systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 32-39.
    14. Elofsson, Katarina & Bengtsson, Goran & Gren, Ing-Marie, 2011. "Optimal Management of Invasive Species with Different Reproduction and Survival Strategies," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114343, European Association of Agricultural Economists.
    15. repec:lib:0000of:v:2:y:2016:i:1:p:17-20 is not listed on IDEAS
    16. Batabyal, Saikat, 2021. "COVID-19: Perturbation dynamics resulting chaos to stable with seasonality transmission," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    17. M-Mahdi Naddaf-Sh & Harley Myler & Hassan Zargarzadeh, 2018. "Design and Implementation of an Assistive Real-Time Red Lionfish Detection System for AUV/ROVs," Complexity, Hindawi, vol. 2018, pages 1-10, November.
    18. Costello, Christopher & Springborn, Michael & McAusland, Carol & Solow, Andrew, 2007. "Unintended biological invasions: Does risk vary by trading partner?," Journal of Environmental Economics and Management, Elsevier, vol. 54(3), pages 262-276, November.
    19. Antonín Kouba & Francisco J Oficialdegui & Ross N Cuthbert & Melina Kourantidou & Josie South & Elena Tricarico & Rodolphe E Gozlan & Franck Courchamp & Phillip J Haubrock, 2022. "Identifying economic costs and knowledge gaps of invasive aquatic crustaceans," Post-Print hal-03860579, HAL.
    20. İ. Esra Büyüktahtakın & Robert G. Haight, 2018. "A review of operations research models in invasive species management: state of the art, challenges, and future directions," Annals of Operations Research, Springer, vol. 271(2), pages 357-403, December.
    21. Horsch, Eric J. & Lewis, David J., 2008. "The Effects of Aquatic Invasive Species on Property Values: Evidence from a Quasi-Random Experiment," Staff Papers 92216, University of Wisconsin-Madison, Department of Agricultural and Applied Economics.

    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:chsofr:v:147:y:2021:i:c:s0960077921002836. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.