Controlling Network-Coupled Neural Dynamics with Nonlinear Network Control Theory

Electrical stimulation has been an emerging technique for treating neural disorders. However, the previous studies mainly used empirical methods to select stimulation parameters and linear optimal control theory-based methods to obtain optimal control strategies. This paper offers a feasible solution to the problem of controlling the temporal dynamics of complex nonlinear network-coupled dynamical systems, specifically in terms of neural dynamics. For systems that meet two simple conditions, i.e., Lipschitz continuity and quadratic condition, we derive a control strategy with theoretical guarantees of controllability based on the Lyapunov direct method. To verify the performance of the derived control strategy, we perform numerical experiments on two nonlinear network-coupled dynamical systems that emulate phase synchronization and neural population dynamics. The results of the numerical experiments demonstrate the feasibility and effectiveness of our control strategy when applied to systems that closely resemble real-world systems, which provides robust theoretical and practical insights for future applications.