4.7 Article

Phase diagram of a cyclic predator-prey model with neutral-pair exchange

Journal

PHYSICAL REVIEW E
Volume 88, Issue 2, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.88.022133

Keywords

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Funding

  1. Brazilian Science Agency CNPq [475039/2010-6]
  2. Argentinian Science Agency CONICET
  3. Argentinian Science Agency ANPCyT
  4. Universidade Federal de Santa Catarina (UFSC)
  5. Universidad Nacional de La Plata (UNLP)

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In this paper we obtain the phase diagram of a four-species predator-prey lattice model by using the proposed gradient method. We consider cyclic transitions between consecutive states, representing invasion or predation, and allowed the exchange between neighboring neutral pairs. By applying a gradient in the invasion rate parameter one can see, in the same simulation, the presence of two symmetric absorbing phases, composed by neutral pairs, and an active phase that includes all four species. In this sense, the study of a single-valued interface and its fluctuations give the critical point of the irreversible phase transition and the corresponding universality classes. Also, the consideration of a multivalued interface and its fluctuations bring the percolation threshold. We show that the model presents two lines of irreversible first-order phase transition between the two absorbing phases and the active phase. Depending on the value of the system parameters, these lines can converge into a triple point, which is the beginning of a first-order irreversible line between the two absorbing phases, or end in two critical points belonging to the directed percolation universality class. Standard simulations for some characteristic values of the parameters confirm the order of the transitions as determined by the gradient method. Besides, below the triple point the model presents two standard percolation lines in the active phase and above a first-order percolation transition as already found in other similar models.

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