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

Area of Science:

• Computational Neuroscience
• Nonlinear Dynamics
• Control Theory

Background:

• Hindmarsh-Rose neurons exhibit complex nonlinear dynamics.
• Synchronization of neural systems is crucial for understanding brain function.
• Existing methods struggle with noise and fixed-time convergence.

Purpose of the Study:

• To develop a physics-informed Koopman operator framework for fixed-time synchronization of Hindmarsh-Rose neurons.
• To design a non-singular fixed-time controller robust to noise.
• To incorporate a dynamic event-triggering mechanism for communication efficiency.

Main Methods:

• Koopman operator theory to linearize nonlinear neuronal dynamics in a higher-dimensional space.
• Physics-informed lifting dictionary derived from HR neuron algebraic nonlinearities.
• Non-singular fixed-time control design and dynamic event-triggering mechanism (DETM).

Main Results:

• The proposed framework achieves guaranteed fixed-time synchronization for Hindmarsh-Rose neurons.
• The controller ensures convergence within a predefined time, independent of initial conditions.
• The DETM effectively manages communication bandwidth limitations.

Conclusions:

• The physics-informed Koopman framework provides an effective approach for fixed-time neural synchronization.
• The study demonstrates robustness against mixed Gaussian and Poisson jump noise.
• The developed control strategy is suitable for resource-constrained communication environments.