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Type I Type II, PRCs and Coupling

Type I Type II, PRCs and Coupling. Daniel Forger. Through what mechanism do oscillations appear?. Type 1 Integrator. With such a mechanism. Oscillations abruptly start or stop The period changes drastically when parameters are changed

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Type I Type II, PRCs and Coupling

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

  2. Through what mechanism do oscillations appear?

  3. Type 1 Integrator

  4. 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. Type 2 Resonator

  6. 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. Chaotic Entrainment

  8. Type I vs. Type IIPloS Computational Biology 2:e30

  9. Design I

  10. Design II

  11. Coupling by sharing a protein

  12. Coupling by sharing a protein

  13. Coupling by extracellular signalingGarcia-Ojalvo et al. PNAS 101:10955

  14. Order Parameter

  15. Coupling can reduce noise

  16. Phase ShiftingGlass and Winfree AJP 246:R251

  17. PRC Atlas

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

  19. 0-D phaseless region

  20. 1-D phaseless region

  21. 2-D Phaseless Region

  22. Winfree, The Geometry of Biological Time

  23. Ukai, Nature Cell Biology 9:1327

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