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    Higher order interactions in complex systems influence network dynamics, but their control is challenging. A new model shows these interactions have a modest effect, while feedback control effectively optimizes dynamics.

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    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.