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Experimental Demonstration of Remote Synchronization in Coupled Nonlinear Oscillator

Sanjeev Kumar Pandey

Abstract

This study investigates remote synchronization in scale-free networks of coupled nonlinear oscillators inspired by synchronization observed in the brain's cortical regions and power grid. We employ the Master Stability Function (MSF) approach to analyze network stability across various oscillator models. Synchronization results are obtained for a star network using linearization techniques and extended to arbitrary networks with benchmark oscillators, verifying consistent behavior. Stable synchronous solutions emerge as the Floquet multiplier decreases and the MSF becomes negative. Additionally, we demonstrate remote synchronization in a star network, where peripheral oscillators communicate exclusively through a central hub, drawing parallels to neuronal synchronization in the brain. Experimental validation is achieved through an electronic circuit testbed, supported by nonlinear ODE modeling and LTspice simulation. Future work will extend the investigation to arbitrary network topologies, further elucidating synchronization dynamics in complex systems.

Experimental Demonstration of Remote Synchronization in Coupled Nonlinear Oscillator

Abstract

This study investigates remote synchronization in scale-free networks of coupled nonlinear oscillators inspired by synchronization observed in the brain's cortical regions and power grid. We employ the Master Stability Function (MSF) approach to analyze network stability across various oscillator models. Synchronization results are obtained for a star network using linearization techniques and extended to arbitrary networks with benchmark oscillators, verifying consistent behavior. Stable synchronous solutions emerge as the Floquet multiplier decreases and the MSF becomes negative. Additionally, we demonstrate remote synchronization in a star network, where peripheral oscillators communicate exclusively through a central hub, drawing parallels to neuronal synchronization in the brain. Experimental validation is achieved through an electronic circuit testbed, supported by nonlinear ODE modeling and LTspice simulation. Future work will extend the investigation to arbitrary network topologies, further elucidating synchronization dynamics in complex systems.

Paper Structure

This paper contains 10 sections, 1 theorem, 16 equations, 9 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Mathematical Background
  3. Floquet Theory
  4. Master Stability Function
  5. Remote synchronization results
  6. Example First: Kuramoto oscillator
  7. Example Second: Coupled FHN oscillators using
  8. Remote synchronization of arbitrary network
  9. Experimental results
  10. Conclusion

Key Result

Lemma 2.1

Consider a linear time-varying system governed by the equation $\dot {x}=A(t)x$, where $A(t+T)=A(t)$ for all $t$ and $T$ is a positive constant. Let $\phi(t,t_{0})$ denote the state transition matrix that maps the state at time $t_{0}$ to the state at time $t$, let $\phi(t+T, t)$ be the associated F

Figures (9)

  • Figure 1: Star topology with central Hub and Peripheral node P.
  • Figure 2: Numerical simulations demonstrate the convergence of phase differences to zero between the central and peripheral oscillators and among the peripheral oscillators themselves.
  • Figure 3: Figure illustrates the Gershgorin discs corresponding to the Jacobian matrix.
  • Figure 4: Fig. (a) illustrates complete synchronization between the mediator (hub oscillator) and mediated oscillators (peripheral oscillators). Fig. (b) depicts the convergence of phase differences between oscillators to zero, indicating phase synchronization.
  • Figure 5: Graph with five nodes
  • ...and 4 more figures

Theorems & Definitions (1)

  • Lemma 2.1