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Demonstrating Remote Synchronization: An Experimental Approach with Nonlinear Oscillators

Sanjeev Kumar Pandey, Neetish Patel

TL;DR

This work addresses remote synchronization in arbitrary clusters of nonlinear oscillators, linking neural-like coordination to engineered networks. It combines Lyapunov-Floquet transformation and Master Stability Function analysis with numerical simulations of coupled Van der Pol oscillators and experimental LTSpice/breadboard validation. The results show that increasing the coupling parameter $\kappa$ (via $\kappa \lambda_{\max}$) decreases the maximum Floquet multiplier $\mu_{\max}$, yielding stable synchronization across mediator-enabled clusters. The study provides a rigorous analytical framework and practical demonstrations, suggesting potential applications in neuroscience, communication networks, and power systems, and outlines directions for exploring diverse network topologies.

Abstract

This study investigates remote synchronization in arbitrary network clusters of coupled nonlinear oscillators, a phenomenon inspired by neural synchronization in the brain. Employing a multi-faceted approach encompassing analytical, numerical, and experimental methodologies, we leverage the Master Stability Function (MSF) to analyze network stability. We provide experimental evidence of remote synchronization between two clusters of nonlinear oscillators, where oscillators within each cluster are also remotely connected. This observation parallels the thalamus-mediated synchronization of neuronal populations in the brain. An electronic circuit testbed, supported by nonlinear ODE modeling and LT Spice simulation, was developed to validate our theoretical predictions. Future work will extend this investigation to encompass diverse network topologies and explore potential applications in neuroscience, communication networks, and power systems.

Demonstrating Remote Synchronization: An Experimental Approach with Nonlinear Oscillators

TL;DR

This work addresses remote synchronization in arbitrary clusters of nonlinear oscillators, linking neural-like coordination to engineered networks. It combines Lyapunov-Floquet transformation and Master Stability Function analysis with numerical simulations of coupled Van der Pol oscillators and experimental LTSpice/breadboard validation. The results show that increasing the coupling parameter (via ) decreases the maximum Floquet multiplier , yielding stable synchronization across mediator-enabled clusters. The study provides a rigorous analytical framework and practical demonstrations, suggesting potential applications in neuroscience, communication networks, and power systems, and outlines directions for exploring diverse network topologies.

Abstract

This study investigates remote synchronization in arbitrary network clusters of coupled nonlinear oscillators, a phenomenon inspired by neural synchronization in the brain. Employing a multi-faceted approach encompassing analytical, numerical, and experimental methodologies, we leverage the Master Stability Function (MSF) to analyze network stability. We provide experimental evidence of remote synchronization between two clusters of nonlinear oscillators, where oscillators within each cluster are also remotely connected. This observation parallels the thalamus-mediated synchronization of neuronal populations in the brain. An electronic circuit testbed, supported by nonlinear ODE modeling and LT Spice simulation, was developed to validate our theoretical predictions. Future work will extend this investigation to encompass diverse network topologies and explore potential applications in neuroscience, communication networks, and power systems.

Paper Structure

This paper contains 9 sections, 1 theorem, 8 equations, 7 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Remote synchronization
  3. Remote Interaction in Arbitrarily Coupled Networks
  4. Mathematical Approaches for Analyzing Remote Synchronization in Complex Systems
  5. Lyapunov-Floquet transformation algorithm
  6. Master Stability Function
  7. Numerical simulation
  8. Experimental results
  9. Conclusion

Key Result

Lemma 2.1

Consider a network of $N$ coupled identical dynamical systems with individual node dynamics governed by the equation where $\psi(\chi_i)$ represents the intrinsic node dynamics, $g(\chi_j)=H(\chi_{j}-\chi_{i})$ denotes the coupling function, $\kappa$ is the coupling strength, and $L$ is the Laplacian matrix of the network. Assume that the network is in a synchronized state such that $\chi_1(t) =

Figures (7)

  • Figure 1: Remotely connected network
  • Figure 2: Coupled two arbitrary network by mediaters (x2,y2).
  • Figure 3: Numerical simulation of remote synchronization for the arbitrary coupled oscillators.
  • Figure 4: Numerical simulation indicates that the Master Stability Function of a connected VPO exhibits a decreasing $\mu_{max}$ with increasing ($\kappa$).
  • Figure 5: Circuit diagram of a coupled Van der Pol oscillator network with arbitrary topology designed in LT Spice simulation.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Lemma 2.1