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: gsyn 12 = 0.1 gsyn 21 = 0.1 gsyn 23 = 0.1 gsyn 32 = 0.1 gsyn 31 = 0.1 gsyn 13 = 0.1 Coupling strengths are identical between neurons in both clockwise and counterclockwise directions.

9. Synchronization Diagram Blue, Red in phase Green out of phase Legend Red, Green in phase Blue out of phase Blue, Green in phase Red 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:

10. Strongly coupled motif – asymmetric case: Coupling strengths are significantly stronger in the counter-clockwise direction than in the clockwise direction. gsyn 12 = 0.8 gsyn 21 = 0.2 gsyn 23 = 0.8 gsyn 32 = 0.2 gsyn 31 = 0.8 gsyn 13 = 0.2

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

12. Strongly coupled motif – discussion:

13. Weakly coupled motif: gsyn 12 = 0.0005 gsyn 21 = 0.0005 gsyn 23 = 0.0005 gsyn 32 = 0.0005 gsyn 31 = 0.0005 gsyn 13 = 0.0005 Coupling strengths are identical between neurons in both clockwise and counterclockwise directions.

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