IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v580y2021ics0378437121004106.html
   My bibliography  Save this article

Population dynamics for systems with cyclic predator–prey relations and pheromone dependent movement

Author

Listed:
  • Kayacan, O.
  • Middendorf, M.

Abstract

Predator-prey dynamics is an important field of study to understand population dynamics in ecosystems. In nature, some predators use olfactory information, e.g., pheromone released by the prey, to locate their prey. Population dynamics is investigated in this paper for the case of three species with cyclic predator–prey relations and (artificial) pheromone on a one-dimensional lattice. Using computer simulations we study a three-species model for different pheromone evaporation rates. The results reveal that the survival of three species depends on the evaporation rate. At a sufficiently low evaporation rate and high densities, a phase transition takes place. Before the phase transition, three species coexist at the same time. After the phase transition, however, two species are extinct and only one species survives. For a sufficiently high value of evaporation rate, there does not happen a phase transition and three species coexist at all densities. The critical density at which phase transition takes place depends on the value of the evaporation rate.

Suggested Citation

  • Kayacan, O. & Middendorf, M., 2021. "Population dynamics for systems with cyclic predator–prey relations and pheromone dependent movement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
  • Handle: RePEc:eee:phsmap:v:580:y:2021:i:c:s0378437121004106
    DOI: 10.1016/j.physa.2021.126137
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121004106
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2021.126137?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. Nagatani, Takashi & Ichinose, Genki & Tainaka, Kei-ichi, 2018. "Traffic jams induce dynamical phase transition in spatial rock–paper–scissors game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1081-1087.
    2. Tobias Reichenbach & Mauro Mobilia & Erwin Frey, 2007. "Mobility promotes and jeopardizes biodiversity in rock–paper–scissors games," Nature, Nature, vol. 448(7157), pages 1046-1049, August.
    3. Larry Samuelson, 2002. "Evolution and Game Theory," Journal of Economic Perspectives, American Economic Association, vol. 16(2), pages 47-66, Spring.
    4. Bernd Blasius & Amit Huppert & Lewi Stone, 1999. "Complex dynamics and phase synchronization in spatially extended ecological systems," Nature, Nature, vol. 399(6734), pages 354-359, May.
    5. Kayacan, Ozhan, 2011. "A theoretical model for uni-directional ant trails," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(6), pages 1111-1116.
    6. Binmore, Ken & Swierzbinski, Joe & Proulx, Chris, 2001. "Does Minimax Work? An Experimental Study," Economic Journal, Royal Economic Society, vol. 111(473), pages 445-464, July.
    7. Benjamin Kerr & Margaret A. Riley & Marcus W. Feldman & Brendan J. M. Bohannan, 2002. "Local dispersal promotes biodiversity in a real-life game of rock–paper–scissors," Nature, Nature, vol. 418(6894), pages 171-174, July.
    8. Cheung, Yin-Wong & Friedman, Daniel, 1998. "A comparison of learning and replicator dynamics using experimental data," Journal of Economic Behavior & Organization, Elsevier, vol. 35(3), pages 263-280, April.
    9. John Van Huyck & Frederick Rankin & Raymond Battalio, 1999. "What Does it Take to Eliminate the use of a Strategy Strictly Dominated by a Mixture?," Experimental Economics, Springer;Economic Science Association, vol. 2(2), pages 129-150, December.
    Full references (including those not matched with items on IDEAS)

    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. Xu, Bin & Zhou, Hai-Jun & Wang, Zhijian, 2013. "Cycle frequency in standard Rock–Paper–Scissors games: Evidence from experimental economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4997-5005.
    2. Park, Junpyo, 2022. "Effect of external migration on biodiversity in evolutionary dynamics of coupled cyclic competitions," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    3. Menezes, J. & Moura, B., 2022. "Pattern formation and coarsening dynamics in apparent competition models," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. Yang, Ryoo Kyung & Park, Junpyo, 2023. "Evolutionary dynamics in the cyclic competition system of seven species: Common cascading dynamics in biodiversity," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    5. Bazeia, D. & Bongestab, M. & de Oliveira, B.F. & Szolnoki, A., 2021. "Effects of a pestilent species on the stability of cyclically dominant species," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    6. Menezes, J. & Barbalho, R., 2023. "How multiple weak species jeopardise biodiversity in spatial rock–paper–scissors models," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    7. Dai, Hui & Wang, Xiaoyue & Lu, Yikang & Hou, Yunxiang & Shi, Lei, 2024. "The effect of intraspecific cooperation in a three-species cyclic predator-prey model," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    8. Mohd, Mohd Hafiz & Park, Junpyo, 2021. "The interplay of rock-paper-scissors competition and environments mediates species coexistence and intriguing dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    9. Zhong, Linwu & Zhang, Liming & Li, Haihong & Dai, Qionglin & Yang, Junzhong, 2022. "Species coexistence in spatial cyclic game of five species," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    10. Zhang, Jing & Li, Zhao & Zhang, Jiqiang & Ma, Lin & Zheng, Guozhong & Chen, Li, 2023. "Emergence of oscillatory cooperation in a population with incomplete information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    11. Wang, Yijia & Chen, Xiaojie & Wang, Zhijian, 2017. "Testability of evolutionary game dynamics based on experimental economics data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 455-464.
    12. Avelino, P.P. & de Oliveira, B.F. & Trintin, R.S., 2022. "Parity effects in rock-paper-scissors type models with a number of species NS≤12," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    13. Huang, Wenting & Duan, Xiaofang & Qin, Lijuan & Park, Junpyo, 2023. "Fitness-based mobility enhances the maintenance of biodiversity in the spatial system of cyclic competition," Applied Mathematics and Computation, Elsevier, vol. 456(C).
    14. Tenorio, M. & Rangel, E. & Menezes, J., 2022. "Adaptive movement strategy in rock-paper-scissors models," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    15. Bazeia, D. & Bongestab, M. & de Oliveira, B.F., 2022. "Influence of the neighborhood on cyclic models of biodiversity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    16. Verma, Tina & Gupta, Arvind Kumar, 2021. "Evolutionary dynamics of rock-paper-scissors game in the patchy network with mutations," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    17. Zhang, Libin & Yao, Zijun & Wu, Bin, 2021. "Calculating biodiversity under stochastic evolutionary dynamics," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    18. Zhang, Zeyu & Bearup, Daniel & Guo, Guanming & Zhang, Helin & Liao, Jinbao, 2022. "Competition modes determine ecosystem stability in rock–paper–scissors games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    19. Zhijian Wang & Shujie Zhou & Qinmei Yao & Yijia Wang, 2022. "Dynamic Structure in Four-strategy Game: Theory and Experiment," Papers 2203.14669, arXiv.org.
    20. Ge, Zheng-Ming & Chang, Ching-Ming & Chen, Yen-Sheng, 2006. "Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1298-1315.

    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:phsmap:v:580:y:2021:i:c:s0378437121004106. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.