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<p>This study proposes a physics-informed Koopman operator framework for the fixed-time (FXT) synchronization of Hindmarsh-Rose (HR) neurons subject to mixed Gaussian and Poisson jump noise. This paper introduces the Koopman operator to lift the nonlinear neuronal dynamics into a higher dimensional space where the evolution becomes globally linear. Distinct to the data-driven methods which rely on genric basis functions, this paper design a physics-informed lifting dictionary explicitly derived from the governing algebraic nonlinearities of the HR dynamics. Based on the proposed lifted framework, this study designs a non-singular FXT controller which guarantees the convergence within a pre-determined settling time, independent of the initial error states. Further, the communication bandwidth limitations are handled through a dynamic event-triggering mechanism (DETM) ensuring the control actions are executed only when the event-triggering condition is satisfied. The numerical simulations are performed to validate the performance of the proposed theoretical frameworks.</p>

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Physics-informed Koopman learning approach for fixed-time synchronization of stochastic neural dynamics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月3日

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  • Mubasil P,
  • Prakash Mani

摘要

This study proposes a physics-informed Koopman operator framework for the fixed-time (FXT) synchronization of Hindmarsh-Rose (HR) neurons subject to mixed Gaussian and Poisson jump noise. This paper introduces the Koopman operator to lift the nonlinear neuronal dynamics into a higher dimensional space where the evolution becomes globally linear. Distinct to the data-driven methods which rely on genric basis functions, this paper design a physics-informed lifting dictionary explicitly derived from the governing algebraic nonlinearities of the HR dynamics. Based on the proposed lifted framework, this study designs a non-singular FXT controller which guarantees the convergence within a pre-determined settling time, independent of the initial error states. Further, the communication bandwidth limitations are handled through a dynamic event-triggering mechanism (DETM) ensuring the control actions are executed only when the event-triggering condition is satisfied. The numerical simulations are performed to validate the performance of the proposed theoretical frameworks.