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Assembly and Characterization of an External Driver for the Generation of Sub-Kilohertz Oscillatory Flow in Microchannels
Published on: January 28, 2022
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Arnold tongues in oscillator systems with nonuniform spatial driving
Alexander Golden1,2, Allyson E Sgro2,3, Pankaj Mehta1,2
1Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Physical Review. E
|May 19, 2021
Summary
Controlling spatially coupled nonlinear oscillators is key in many systems. Spatially structured drives can precisely control oscillator synchronization, offering new methods for biological and physical applications.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Theoretical Physics
- Biophysics
Background:
- Nonlinear oscillator systems are fundamental in diverse scientific fields, including physics and biology.
- Controlling the behavior of coupled oscillators is a significant challenge in experimental setups.
- Existing models often lack spatial coupling or external medium interactions, limiting applicability.
Purpose of the Study:
- To investigate the control of spatially coupled nonlinear oscillator systems using external drives.
- To analyze the effects of spatially and temporally varying control signals on oscillator synchronization.
- To compare the dynamics of the complex Ginzburg-Landau equation (CGLE) and an external medium-coupled CGLE (emCGLE).
Main Methods:
- Mathematical modeling of spatially coupled oscillators, including the CGLE and emCGLE.
- Analysis of external control drives with spatial and temporal variations.
- Investigation of bifurcation structures and synchronization phenomena.
- Comparison with the driven Kuramoto model to understand the role of spatial structure.
Main Results:
- The spatial distribution of control drives critically determines the frequency ranges for oscillator synchronization.
- Boundary conditions significantly impact synchronization in the CGLE model.
- The emCGLE exhibits a low-density regime allowing broad frequency synchronization with low drive amplitudes.
- Bifurcation structures of the studied models closely resemble those of the spatially unstructured driven Kuramoto model.
Conclusions:
- Spatially structured external drives offer effective control over coupled nonlinear oscillator systems.
- The emCGLE model provides enhanced control capabilities, particularly in low-density regimes.
- These findings have implications for controlling biological systems like Dictyostelium and chemical systems like Belousov Zhabotinsky reactions.
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