Phase Bursting Rhythms in Inhibitory Rings

Matthew BrooksAndrey ShilnikovRobert Clewley

13 May 2009

Introduction

Phase shift bursting

Inhibitory ring systems

The Leech Heart Interneuron

Computing phase rhythms

Computing phase rhythms, cont’d.

Strongly coupled motif - symmetric case:

gsyn12 = 0.1gsyn21 = 0.1gsyn23 = 0.1gsyn32 = 0.1gsyn31 = 0.1gsyn13 = 0.1

Coupling strengths are identical between neurons in both clockwise and counterclockwise directions.

Synchronization Diagram

Blue, Red in phaseGreen out of phase

Legend

Red, Green in phaseBlue out of phase

Blue, Green in phaseRed out of phase

Plot indicating which neurons are “in phase” and which ones are “out of phase”.

All neurons are out of phase.

Strongly coupled motif - symmetric case, cont’d:

Strongly coupled motif – asymmetric case:Coupling strengths are significantly stronger in the counter-clockwise direction than in the clockwise direction.

gsyn12 = 0.8gsyn21 = 0.2gsyn23 = 0.8gsyn32 = 0.2gsyn31 = 0.8gsyn13 = 0.2

Strongly coupled motif – asymmetric case, cont’d:

Strongly coupled motif – discussion:

Weakly coupled motif:

gsyn12 = 0.0005gsyn21 = 0.0005gsyn23 = 0.0005gsyn32 = 0.0005gsyn31 = 0.0005gsyn13 = 0.0005

Coupling strengths are identical between neurons in both clockwise and counterclockwise directions.

Synchronization DiagramPlot indicating which neurons are “in phase” and which ones are “out of phase”.

Weakly coupled motif, cont’d:

Blue, Red in phaseGreen out of phase

Legend

Red, Green in phaseBlue out of phase

Blue, Green in phaseRed out of phase All neurons are out of phase.

Weakly coupled motif, cont’d:

Weakly coupled motif - discussion:

Discussion of Results and Observations:

References:

Thank you: