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Experimental chaotic synchronization for coupled double pendula.

Dawid Dudkowski¹, Jerzy Wojewoda¹, Krzysztof Czołczyński¹

¹Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland.

Chaos (Woodbury, N.Y.)

|July 9, 2021

Summary

This summary is machine-generated.

This study experimentally verifies chaotic synchronization in coupled forced oscillators, specifically three double pendula. Stronger coupling enhances synchronization precision while preserving the chaotic nature of the system.

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Area of Science:

Physics
Nonlinear Dynamics
Complex Systems

Background:

Coupled oscillators exhibit complex behaviors, including synchronization.
Chaotic dynamics in mechanical systems like pendula are of significant interest.
Understanding synchronization in chaotic systems is crucial for various applications.

Purpose of the Study:

To experimentally verify chaotic synchronization in a system of three coupled forced double pendula.
To investigate the relationship between coupling strength and synchronization precision.
To identify factors influencing synchronization and desynchronization in chaotic coupled oscillators.

Main Methods:

Experimental setup involving three double pendula connected by springs.
Varying external excitation parameters to induce periodic and chaotic behavior.
Measuring synchronization precision by analyzing differences in pendulum bob motion.
Numerical simulations to confirm experimental findings.

Main Results:

Demonstrated practical chaotic synchronization in the coupled double pendulum system.
Showed that increased coupling strength improves synchronization precision.
Identified pendulum parameters and coupling strength as key factors affecting synchronization.
Proposed a mechanism for desynchronization involving unstable stationary points and transient dynamics.

Conclusions:

Chaotic synchronization is achievable and controllable in coupled forced pendula systems.
The chaotic nature of individual oscillators is preserved during practical synchronization.
The findings have implications for understanding and designing complex coupled systems with chaotic dynamics.