Higher Order Interactions in Hub Neural Networks: Spatiotemporal Dynamics Reshaping and Control

Area of Science:

• Complex Systems Dynamics
• Neural Network Modeling
• Control Theory

Background:

• Traditional network analysis focuses on pairwise interactions, neglecting higher order interactions (three or more units).
• The role of higher order interactions in biological neural networks and their control remains poorly understood.
• Existing models often simplify or omit these collective influences.

Purpose of the Study:

• To propose a novel controlled diffusion hub neural network model incorporating higher order interactions.
• To introduce a cross-node associated delayed feedback control (CNADFC) method for regulating spatiotemporal dynamics.
• To analyze the impact of higher order interactions and control strategies on network stability and emergent patterns.

Main Methods:

• Development of a diffusion hub neural network model with explicit higher order interaction terms.
• Application of cross-node associated delayed feedback control (CNADFC) for dynamic regulation.
• Mathematical analysis of local stability, Turing instability, and Hopf bifurcation.
• Numerical simulations to validate theoretical findings and explore parameter effects.

Main Results:

• Turing instability was found to be unattainable in this model.
• Spatially periodic patterns emerge under specific parametric conditions.
• Self-feedback, control, and first-order interactions significantly impact stability and dynamics.
• Higher order interactions demonstrated a comparatively modest influence on overall network behavior.

Conclusions:

• The proposed model provides insights into diffusion neural network dynamics with higher order interactions.
• The CNADFC method offers an effective means to optimize spatiotemporal dynamics in such networks.
• This research advances the understanding and control of complex systems with collective influences.