Dynamics due to competitive flip cycles in active Potts models.

Area of Science:

• Complex Systems
• Statistical Physics
• Nonlinear Dynamics

Background:

• Nonequilibrium spatiotemporal patterns are widely studied.
• Previous models typically use single oscillators or cyclic loops at each site.
• The influence of multiple interacting cyclic loops remains underexplored.

Purpose of the Study:

• To investigate how competition among multiple identical cyclic loops at each site affects pattern formation.
• To explore the role of flip energy and network topology in emergent patterns.
• To determine if spatial coexistence of states can be controlled.

Main Methods:

• Simulations using active Potts models on two-dimensional square lattices.
• Modeling standard Potts interactions between neighboring sites.
• Varying the number of states in cyclic loops (three-state and four-state) and flip energies.

Main Results:

• Multiple three-state cycles can form simultaneous spiral waves at high flip energies.
• At lower energies, spiral waves and homogeneous cycling (HC) modes emerge, with stochastic switching between types.
• Four-state cycles lead to a dominant state with occasional domain formation of other states.
• Spiral wave and HC modes can coexist temporally in small systems but not in large systems.

Conclusions:

• The number of spatially coexisting states is controllable.
• Flip networks and energies are key parameters for tuning pattern complexity.
• This work provides insights into controlling complex emergent behaviors in spatially extended systems.