Robust complete synchronization of electrical coupling neurons under uncertain heterogeneous disturbances using...

Area of Science:

• Computational Neuroscience
• Control Theory
• Nonlinear Dynamics

Background:

• Coupled neuronal models like FitzHugh-Nagumo (FHN) exhibit complex dynamics.
• Achieving robust synchronization in FHN neurons is challenging due to external disturbances.
• Internal model control offers a framework for handling system uncertainties.

Purpose of the Study:

• To develop a robust complete synchronization strategy for two gap-junction coupled FHN neurons.
• To address uncertain and heterogeneous disturbances affecting neuronal synchronization.
• To design an adaptive control method ensuring stability and synchronization.

Main Methods:

• An adaptive internal model control strategy was designed.
• The synchronization problem was reformulated as a robust stabilization of an augmented system.
• An adaptive law was employed to estimate the internal model under disturbances.
• A state-feedback stabilizer was designed for asymptotic stability.

Main Results:

• The proposed adaptive internal model control strategy achieved robust complete synchronization.
• The adaptive law successfully estimated the internal model despite uncertain disturbances.
• The designed state-feedback stabilizer guaranteed the asymptotic stability of the closed-loop system.
• Simulation results validated the effectiveness of the proposed method.

Conclusions:

• The adaptive internal model control is effective for robust synchronization of coupled FHN neurons.
• The method provides a reliable approach for handling uncertain disturbances in neuronal systems.
• The study demonstrates the potential of adaptive control in computational neuroscience applications.