Phase Bursting Rhythms in Inhibitory Rings

1. Phase Bursting Rhythms in Inhibitory Rings Matthew Brooks Andrey Shilnikov Robert Clewley 13 May 2009

2. Introduction

3. Phase shift bursting

4. Inhibitory ring systems

5. The Leech Heart Interneuron

6. Computing phase rhythms

7. Computing phase rhythms, cont’d.

8. Strongly coupled motif - symmetric case: Coupling strengths are identical between neurons in both clockwise and counterclockwise directions. gsyn12 = 0.1 gsyn21 = 0.1 gsyn23 = 0.1 gsyn32 = 0.1 gsyn31 = 0.1 gsyn13 = 0.1

9. SynchronizationDiagram Strongly coupled motif - symmetric case, cont’d: Plot indicating which neurons are “in phase” and which ones are “out of phase”. Legend Blue, Red in phase Green out of phase Red, Green in phase Blue out of phase Blue, Green in phase Red out of phase All neurons are out of phase.

10. Strongly coupled motif – asymmetric case: Coupling strengths are significantly stronger in the counter-clockwise direction than in the clockwise direction. gsyn12 = 0.8 gsyn21 = 0.2 gsyn23 = 0.8 gsyn32 = 0.2 gsyn31 = 0.8 gsyn13 = 0.2

11. Strongly coupled motif – asymmetric case, cont’d:

12. Strongly coupled motif – discussion:

13. Weakly coupled motif: Coupling strengths are identical between neurons in both clockwise and counterclockwise directions. gsyn12 = 0.0005 gsyn21 = 0.0005 gsyn23 = 0.0005 gsyn32 = 0.0005 gsyn31= 0.0005 gsyn13= 0.0005

14. SynchronizationDiagram Weakly coupled motif, cont’d: Plot indicating which neurons are “in phase” and which ones are “out of phase”. Legend Blue, Red in phase Green out of phase Red, Green in phase Blue out of phase Blue, Green in phase Red out of phase All neurons are out of phase.

15. Weakly coupled motif, cont’d:

16. Weakly coupled motif - discussion:

17. Discussion of Results and Observations:

18. References:

19. Thank you: