Macroscopic coherent structures in a stochastic neural network: from interface dynamics to coarse-grained bifurcation...

Area of Science:

• Computational neuroscience
• Complex systems
• Mathematical biology

Background:

• Neural network models are crucial for understanding brain function.
• Cellular automata provide a framework for simulating large-scale neural activity.
• Previous work established models supporting localized activity patterns.

Purpose of the Study:

• To analyze coarse pattern formation in a spatially-extended stochastic neural network model.
• To investigate the existence and stability of stationary and traveling activity patterns.
• To bridge analytical and computational approaches for understanding neural dynamics.

Main Methods:

• Utilized a cellular automaton model of a stochastic neural network.
• Employed analytical techniques (interface methods, probability mass functions) in deterministic and stochastic limits.
• Applied equation-free methods and lifting procedures on a discrete lattice for the full stochastic model.

Main Results:

• Identified synaptic profile as a mesoscopic variable and activity width as a macroscopic variable.
• Characterized stationary and traveling bumps, noting similarities in meso/macroscopic profiles but differences in microscopic structure.
• Provided evidence that traveling waves depend on high synaptic gain and long refractory periods, while meandering bumps require short refractory periods.

Conclusions:

• The study successfully models and analyzes coarse pattern formation in stochastic neural networks.
• Distinct conditions governing traveling waves and meandering bumps were elucidated.
• The proposed lifting operators effectively disambiguate different pattern types using microscopic details.