Finite-Size Effects on Traveling Wave Solutions to Neural Field Equations

Area of Science:

• Computational neuroscience
• Mathematical biology
• Statistical physics

Background:

• Neural field equations model large-scale neural activity.
• Current models often use continuum approximations, neglecting finite-size effects.
• Understanding these effects is crucial for accurate neural network modeling.

Purpose of the Study:

• To explicitly derive neural field equations from discrete neural networks.
• To quantify finite-size effects on neural activity and traveling waves.
• To develop a well-posed stochastic neural field equation.

Main Methods:

• Extending the Bressloff and Newby model.
• Describing discrete network evolution using Markov chains.
• Analyzing Markov chain fluctuations to approximate diffusion processes.
• Investigating the strong continuum limit.

Main Results:

• Finite-size effects, deviations from mean-field predictions, are analyzed.
• A stochastic neural field equation is derived.
• The derived equation incorporates a noise term for finite-size effects.
• This model accurately describes traveling wave solutions.

Conclusions:

• The study provides a rigorous derivation of neural field equations.
• Finite-size effects are crucial and can be modeled stochastically.
• The developed stochastic neural field equation offers improved accuracy for neural network dynamics.