Dynamic pattern formation and collisions in networks of excitable elements.

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Computational Neuroscience

Background:

• Spatially extended excitable systems exhibit resting, activated, and refractory states.
• These systems are known for emergent localized propagating patterns, common in natural phenomena.
• Recent studies highlight neural systems with localized propagating patterns.

Purpose of the Study:

• To introduce and analyze a unique three-state excitable network model.
• To investigate the generation of dynamic patterns and collective dynamics.
• To explore pattern propagation and collision behaviors in excitable media.

Main Methods:

• Development of a novel three-state excitable network model.
• Analysis of symmetry breaking effects on pattern formation.
• Simulation and observation of pattern propagation and collision dynamics.

Main Results:

• The model generates rich collective dynamics and localized propagating patterns.
• Symmetry breaking induces a transition from subdiffusive wandering to superdiffusive propagation.
• The model exhibits diverse collision dynamics between patterns and refractory wakes.

Conclusions:

• The three-state excitable network model effectively reproduces complex dynamics observed in natural systems.
• The findings offer insights into pattern formation and propagation mechanisms.
• This work provides a framework for understanding neural system dynamics and other excitable media.