Phase transitions and oscillations in a lattice prey-predator model

Area of Science:

• Complex Systems
• Ecological Modeling
• Statistical Physics

Background:

• Prey-predator systems are fundamental to ecology.
• Understanding population dynamics requires robust models.
• Lattice models offer a framework for spatial ecological interactions.

Purpose of the Study:

• To describe a coarse-grained, two-dimensional prey-predator system using a three-state lattice model.
• To investigate the model's properties using dynamical mean-field approximations and numerical simulations.
• To analyze phase transitions and oscillatory behaviors within the system.

Main Methods:

• Development of a three-state lattice model for prey-predator interactions.
• Application of dynamical mean-field approximations.
• Conducting extensive numerical simulations.
• Analysis of stationary state phase diagrams and transition types.

Main Results:

• The phase diagram shows a pure prey phase and a coexistence phase with potential oscillations.
• The system exhibits directed percolation-like transitions and a novel transition to a prey absorbing phase.
• Oscillatory and non-oscillatory domains within the coexistence phase are characterized by crossover phenomena.
• Scaling relations and finite size effects are analyzed.

Conclusions:

• The lattice model effectively captures complex prey-predator dynamics, including oscillations.
• Novel phase transitions beyond typical directed percolation are identified.
• The study provides physical insights into the mechanisms driving local and global oscillations in ecological systems.