Memory-dependent bistability and criticality in a stochastic Wilson-Cowan model.

Area of Science:

• Computational Neuroscience
• Theoretical Neuroscience
• Complex Systems

Background:

• The standard Wilson-Cowan model is a foundational tool for understanding neural population dynamics.
• Existing models often assume Markovian processes, limiting their ability to capture memory effects inherent in multistep neural transitions.

Purpose of the Study:

• To develop a novel stochastic Wilson-Cowan model that explicitly incorporates memory from multistep state transitions.
• To analyze the impact of memory on neural network dynamics, including phase transitions and critical phenomena.

Main Methods:

• Introduction of effective transition rates to convert a non-Markov network into an equivalent Markov network.
• Analysis of the system's phase diagram in parameter space.
• Investigation of avalanche dynamics and universality classes.

Main Results:

• Identification of memory-dependent criticality (second-order phase transition) and bistability (first-order phase transition).
• Characterization of a memory-mediated tricritical point separating these regimes.
• Observation of scale-free, memory-dependent avalanches at the critical point, consistent with the directed percolation universality class.
• Demonstration of memory-induced switching between neural states in small networks.

Conclusions:

• Memory is a critical factor influencing neural network behavior, leading to distinct phase transitions and dynamic regimes.
• The developed model provides a framework for studying memory's role in neural computation and collective dynamics.
• This work advances theoretical neuroscience by offering a more realistic representation of neural systems with memory.