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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Larry Samuelson, 2002. "Evolution and Game Theory," Journal of Economic Perspectives, American Economic Association, vol. 16(2), pages 47-66, Spring.
    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. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

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