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    This study introduces a new method to analyze complex dynamics in nonlinear networks using memristors, memcapacitors, and meminductors. The approach enhances understanding of neuromorphic systems and advanced computing primitives.

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    Area of Science:

    • Nonlinear dynamics
    • Emerging nanoscale devices
    • Neuromorphic engineering

    Background:

    • Memristors, memcapacitors, and meminductors (mem-elements) are crucial for advanced computing systems.
    • Analyzing complex dynamics in networks with these elements is challenging.

    Purpose of the Study:

    • To develop a systematic methodology for analyzing complex dynamics in nonlinear networks with mem-elements.
    • To extend the flux-charge analysis method (FCAM) to include memcapacitors and meminductors.

    Main Methods:

    • Derivation of constitutive relations and equivalent circuits in the flux-charge domain for mem-elements.
    • Obtaining state equation descriptions for relevant network subclasses.
    • Analytical study of invariant manifolds, reduced-order dynamics, and bifurcations without parameters.

    Main Results:

    • Identification of invariant manifolds in autonomous networks.
    • Demonstration of infinitely many reduced-order dynamics coexisting on manifolds.
    • Analysis of bifurcations triggered by initial conditions.

    Conclusions:

    • The developed methodology provides a comprehensive understanding of complex dynamics in mem-element networks.
    • This work is fundamental for advancing neuromorphic systems and mem-computing architectures.