Synchronization of oscillators via active media

Area of Science:

• Computational Neuroscience
• Nonlinear Dynamics
• Systems Biology

Background:

• Oscillators and excitable cells are fundamental components in biological and physical systems.
• Understanding their coupled dynamics is crucial for deciphering complex emergent behaviors.

Purpose of the Study:

• To investigate the phase locking and synchronization phenomena in systems of coupled oscillators and excitable cells.
• To analyze the complex dynamics arising from indirect coupling through excitable media.

Main Methods:

• Development of a scalar phase model for coupled oscillators and excitable cells.
• Analysis of system dynamics under varying numbers of excitable and oscillatory components.
• Application of weak-coupling analysis and bifurcation theory.
• Simulation of a gap-junction coupled system of Morris-Lecar neurons.

Main Results:

• One excitable and one oscillatory cell exhibit diverse m:n phase locking.
• Two coupled oscillators interacting via one excitable cell synchronize.
• Coupling via two excitable cells leads to complex dynamics, including bistability and chaos.
• Long chains of excitable cells enhance frequency-difference-dependent locking robustness.

Conclusions:

• The indirect coupling of oscillators via excitable cells can lead to a rich spectrum of dynamical behaviors.
• The complexity of the dynamics scales with the number and arrangement of excitable elements.
• The findings are generalizable across different modeling approaches, including biophysical neuron models.