Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Controlling network-coupled neural dynamics with nonlinear network control theory

Zhongye Xia, Weibin Li, Zhichao Liang, Kexin Lou, Quanying Liu

TL;DR

This work tackles steering the temporal dynamics of nonlinear network-coupled neural systems by deriving a Lyapunov-based control law with formal stability guarantees under Lipschitz and quadratic growth conditions. By defining a Lyapunov function $V(e)$ and showing $\dot{V}(e) = v_1+v_2+v_3$ can be bounded to $\dot{V}(e) \le \lambda_{max} e^T e$, the authors establish global stabilization to the reference when $\lambda_{max} \le 0$ using a control input $u_i = -{w}_{i} \varPsi {e}_{i}$. The analytical results are complemented by numerical experiments on a Jansen-Rit model and a Kuramoto network to illustrate feasibility, robustness, and applicability to neurostimulation tasks. The approach provides a principled, theoretically grounded pathway for designing targeted interventions in neural networks with potentially personalized control settings.

Abstract

This paper addresses the problem of controlling the temporal dynamics of complex nonlinear network-coupled dynamical systems, specifically in terms of neurodynamics. Based on the Lyapunov direct method, we derive a control strategy with theoretical guarantees of controllability. 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 demonstrate the feasibility and effectiveness of our control strategy.

Controlling network-coupled neural dynamics with nonlinear network control theory

TL;DR

This work tackles steering the temporal dynamics of nonlinear network-coupled neural systems by deriving a Lyapunov-based control law with formal stability guarantees under Lipschitz and quadratic growth conditions. By defining a Lyapunov function and showing can be bounded to , the authors establish global stabilization to the reference when using a control input . The analytical results are complemented by numerical experiments on a Jansen-Rit model and a Kuramoto network to illustrate feasibility, robustness, and applicability to neurostimulation tasks. The approach provides a principled, theoretically grounded pathway for designing targeted interventions in neural networks with potentially personalized control settings.

Abstract

This paper addresses the problem of controlling the temporal dynamics of complex nonlinear network-coupled dynamical systems, specifically in terms of neurodynamics. Based on the Lyapunov direct method, we derive a control strategy with theoretical guarantees of controllability. 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 demonstrate the feasibility and effectiveness of our control strategy.
Paper Structure (9 sections, 1 theorem, 15 equations, 1 figure)

This paper contains 9 sections, 1 theorem, 15 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Problem statement
  3. Analytical results
  4. bound for ${v}_{1}$
  5. bound for ${v}_{2}$
  6. bound for ${v}_{3}$
  7. bound for $\Dot{\operatorname{V}}(e)$
  8. Numerical experiments on application scenarios
  9. Conclusion

Key Result

theorem thmcountertheorem

Let Assumptions assumption1 & assumption2 hold, if ${\lambda}_{max}\leqslant0$, where ${\lambda}_{max}$ is the largest eigenvalue of $\left \lgroup\left \lgroup{\theta}_{f}+c{\theta}_{h} \left \| {L} \otimes {I}_{p}\right \|\ \right \rgroup{I}_{n}-\Phi{W}_{n}\right \rgroup\otimes{I}_{p}$. The networ

Figures (1)

  • Figure 1: Two examples: (Left) Seizure suppression on the double cortical columns Jansen-Rit model. (Right) Phase synchronization on the network-coupled Kuramoto oscillator.

Theorems & Definitions (2)

  • theorem thmcountertheorem
  • proof