1. Type I Type II, PRCs and Coupling
Daniel Forger

2. Through what mechanism do oscillations appear?2

3. Type 1 Integrator 3

4. 4

5. With such a mechanism Oscillations abruptly start or stop
The period changes drastically when parameters are changed
The system does not resonate, instead it needs to get kicked 5

6. Type 2 Resonator 6

7. With such a mechanism
Oscillations switch from decaying very slowly to growing very slowly
The period of the oscillations barely changes when going through the bifurcation
The system “resonates” 7

8. Chaotic Entrainment 8

10. Type I vs. Type II PloS Computational Biology 2:e30

12. Design I

13. Design II

15. Coupling by sharing a protein

16. Coupling by sharing a protein

18. Coupling by extracellular signaling Garcia-Ojalvo et al. PNAS 101:10955

20. Order Parameter

21. Coupling can reduce noise

22. Phase Shifting Glass and Winfree AJP 246:R251

23. PRC Atlas

24. Formula for the PRC Point D is on a limit Cycle
We perturb in the positive horizontal direction

26. 0-D phaseless region

27. 1-D phaseless region

28. 2-D Phaseless Region 28

29. 29

30. Winfree, The Geometry of Biological Time

31. Ukai, Nature Cell Biology 9:1327