Analyzing the spatial dynamics of a prey–predator lattice model with social behavior

• An stochastic lattice prey–predator model with multiple stages is analysed.
• The movement of predators is modelled using a local PSO algorithm.
• Invasion of preys by predators causes a monotonic approach to a fixed point during the transient phase of the model.
• After the transient oscillations caused by the movement of swarms are observed.
• For large lattices the period of the oscillations is preserved.

A lattice prey–predator model is studied. Transition rules applied sequentially describe processes such as reproduction, predation, and death of predators. The movement of predators is governed by a local particle swarm optimization algorithm, which causes the formation of swarms of predators that propagate through the lattice. Starting with a single predator in a lattice fully covered by preys, we observe a wavefront of predators invading the zones dominated by preys; subsequent fronts arise during the transient phase, where a monotonic approach to a fixed point is present. After the transient phase the system enters an oscillatory regime, where the amplitude of oscillations appears to be bounded but is difficult to predict. We observe qualitative similar behavior even for larger lattices. An empirical approach is used to determine the effects of the movement of predators on the temporal dynamics of the system. Our results show that the algorithm used to model the movement of predators increases the proficiency of predators.