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Synchronization in reaction-diffusion systems with multiple pacemakers.

F E Nolet¹, J Rombouts¹, L Gelens¹

¹Laboratory of Dynamics in Biological Systems, Department of Cellular and Molecular Medicine, University of Leuven, 3000 Leuven, Belgium.

Chaos (Woodbury, N.Y.)

|June 4, 2020

Summary

This summary is machine-generated.

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Multiple pacemakers in oscillatory systems compete, influencing wave propagation and synchronization. Their size and frequency determine how the system synchronizes, similar to coupled oscillators.

Area of Science:

Complex Systems
Nonlinear Dynamics
Mathematical Biology

Background:

Spatially extended oscillatory systems can synchronize through entrainment by pacemakers.
Pacemakers are regions with higher oscillation frequencies that drive synchronization via wave propagation.
Real-world systems often feature multiple competing pacemakers.

Purpose of the Study:

To numerically analyze how pacemaker properties affect wave propagation and synchronization in oscillatory media.
To investigate the impact of pacemaker size and intrinsic frequency on synchronization.
To study synchronization in systems with pacemakers embedded in a passive medium.

Main Methods:

Detailed numerical analysis of spatially extended oscillatory systems.

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Simulation of wave propagation originating from pacemakers.

Examination of synchronization phenomena under varying pacemaker characteristics and coupling strengths.

Main Results:

Pacemaker size and intrinsic frequency significantly influence the synchronization properties of the medium.
Synchronization can occur in passive media if pacemaker coupling (distance and diffusion) is sufficiently strong.
The transition to synchronization in passive media resembles that of discrete coupled oscillator systems.

Conclusions:

The properties of competing pacemakers are critical determinants of wave dynamics and overall system synchronization.
Synchronization in passive media is achievable through sufficient coupling, highlighting the role of network structure.
Findings provide insights into synchronization mechanisms in diverse spatially extended systems.