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Bogdanov-Takens singularity in tri-neuron network with time delay.

Xing He, Chuandong Li, Tingwen Huang

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    Summary
    This summary is machine-generated.

    This study models a tri-neuron network with time delays, revealing complex dynamics like bifurcations and chaos. These chaotic networks offer potential for secure color image encryption.

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    Area of Science:

    • Computational neuroscience
    • Dynamical systems theory
    • Nonlinear dynamics

    Background:

    • Functional differential equations model systems with memory or delays.
    • Tri-neuron networks are fundamental units in understanding neural computation.
    • Time delays are crucial in neural systems, influencing network behavior.

    Purpose of the Study:

    • To analyze the complex dynamics of a tri-neuron network with time delays using a functional differential equation.
    • To investigate bifurcations and chaotic behaviors within this neural model.
    • To explore the application of chaotic dynamics for secure image encryption.

    Main Methods:

    • Modeling the tri-neuron network with a retarded functional differential equation.
    • Applying center manifold reduction and normal form theory to analyze Bogdanov-Takens (B-T) bifurcation.
    • Utilizing numerical simulations to validate analytical findings and explore chaotic regimes.

    Main Results:

    • The model exhibits various bifurcations, including pitchfork, Hopf, homoclinic, and double-limit cycles.
    • Analysis of the Bogdanov-Takens singularity reveals rich dynamical possibilities.
    • Chaotic dynamics were observed and numerically confirmed.

    Conclusions:

    • The investigated tri-neuron network model demonstrates complex and diverse dynamical behaviors.
    • Bogdanov-Takens bifurcation analysis provides a framework for understanding transitions in neural activity.
    • A novel algorithm demonstrates the feasibility of using chaotic tri-neuron networks for color image encryption.