Itinerant memory dynamics and global bifurcations in chaotic neural networks

Area of Science:

• Neuroscience
• Complex Systems
• Dynamical Systems

Background:

• Chaotic neural networks exhibit complex dynamics.
• Associative memory models are crucial for understanding information storage and retrieval.
• Chaotic itinerancy is a phenomenon observed in complex systems, including neural networks.

Purpose of the Study:

• To investigate the mechanism generating itinerant memory dynamics in a chaotic neural network.
• To analyze the role of periodic points and attracting sets in chaotic itinerancy.
• To numerically verify the intersection of invariant sets using a novel method.

Main Methods:

• A chaotic neural network model with four neurons and two orthogonal stored patterns was used.
• Analysis focused on the intersection of alpha branches of periodic points.
• A novel numerical method was employed to verify the intersection of invariant sets.

Main Results:

• The study identified the intersection of periodic points and the collapse of attracting sets as key to generating itinerant memory dynamics.
• Numerical verification confirmed the intersection of invariant sets.
• The findings provide a concrete example of chaotic itinerancy in a dynamical associative memory.

Conclusions:

• The mechanism of chaotic itinerant memory dynamics in this network is explained by the intersection of invariant sets.
• The novel numerical method is effective for verifying such intersections.
• This research contributes to understanding complex dynamics in neural networks and associative memory.