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Nonequilibrium phase transition in a lattice prey–predator system

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  • Lipowski, Adam
  • Lipowska, Dorota

Abstract

We study a lattice model of a prey–predator system. Mean-field approximation predicts that the active phase, i.e., one with a finite fraction of preys and predators, is a generic phase of this model. Moreover, within this approximation the model exhibits quasi-oscillations resembling Lotka–Volterra systems. However, Monte Carlo simulations for a one-, two-, and three-dimensional versions of this model do not support this scenario and predict that at a certain value of some parameter the model enters the absorbing state, i.e., a state where the entire population of predators dies out and the model is invaded by preys. Simulations for the one-dimensional version indicate that the transition into the absorbing state belongs to the directed percolation universality class.

Suggested Citation

  • Lipowski, Adam & Lipowska, Dorota, 2000. "Nonequilibrium phase transition in a lattice prey–predator system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 276(3), pages 456-464.
    • Handle: RePEc:eee:phsmap:v:276:y:2000:i:3:p:456-464
    DOI: 10.1016/S0378-4371(99)00482-3
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    Cited by:

    1. Mansour, Mahmoud B.A. & Abobakr, Asmaa H., 2022. "Stochastic differential equation models for tumor population growth," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. El-Gohary, Awad & Al-Ruzaiza, A.S., 2007. "Chaos and adaptive control in two prey, one predator system with nonlinear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 443-453.

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