Adjoint method provides phase response functions for delay-induced oscillations

Physical Review Letters

Volumn 109, Issue 4, 2012, Pages

  Kotani, Kiyoshi ^a   Yamaguchi, Ikuhiro ^a   Ogawa, Yutaro ^a   Jimbo, Yasuhiko ^a   Nakao, Hiroya ^b   Ermentrout, G Bard ^c  

^a UNIVERSITY OF TOKYO   (Japan)

^b TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^c UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADJOINT EQUATIONS; ADJOINT METHODS; BILINEAR FORM; BIOLOGICAL OSCILLATORS; DELAY DIFFERENTIAL EQUATIONS; LIMIT CYCLE; LIMIT CYCLE OSCILLATIONS; MULTI-MODAL; PHASE EQUATION; PHASE RESPONSE; PHASE SPACES; THEORETICAL FRAMEWORK;

EIGENVALUES AND EIGENFUNCTIONS; PHASE SPACE METHODS;

DIFFERENTIAL EQUATIONS;

EID: 84864270428     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.109.044101     Document Type: Article

References (27)

1. F.M. Atay, Complex Time-Delay Systems (Springer-Verlag, Berlin, 2010).
2. B. Balachandran, T. Kalmar-Nagy, and D.E. Gilsinn, Delay Differential Equations: Recent Advances and New Directions (Springer-Verlag, Berlin, 2009).
3. C.T.H. Baker, G.A. Bocharov, and C.A.H. Paul, J. Theor. Med. 1748-670X 1, 117 (1997). 10.1080/10273669708833012
4. Y. Asai, Y. Tasaka, K. Nomura, T. Nomura, M. Casadio, and P. Morasso, PLoS ONE 4, e6169 (2009). POLNCL 1932-6203 10.1371/journal.pone.0006169
5. L. Glass and M.C. Mackey, From Clock to Chaos: the Rhythms of Life (Princeton University Press, Princeton, NJ, 1988).
6. L. Herrgen, S. Ares, L.G. Morelli, C. Schröter, F. Jülicher, and A.C. Oates, Curr. Biol. 20, 1244 (2010). CUBLE2 0960-9822 10.1016/j.cub.2010.06.034
7. J.W. Kim and P.A. Robinson, Phys. Rev. E PLEEE8 1539-3755 75, 031907 (2007). 10.1103/PhysRevE.75.031907
8. I. Yamaguchi, Y. Ogawa, Y. Jimbo, H. Nakao, and K. Kotani, PLoS ONE 6, e26497 (2011). POLNCL 1932-6203 10.1371/journal.pone.0026497
9. W. Mather, M.R. Bennett, J. Hasty, and L.S. Tsimring, Phys. Rev. Lett. 102, 068105 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.068105
10. B. Novák and J.J. Tyson, Nat. Rev. Mol. Cell Biol. 9, 981 (2008). NRMCBP 1471-0072 10.1038/nrm2530
11. Y. Takashima, T. Ohtsuki, A. González, H. Miyachi, and R. Kageyama, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 108, 3300 (2011). 10.1073/pnas.1014418108
12. K. Horikawa, K. Ishimatsu, E. Yoshimoto, S. Kondo, and H. Takeda, Nature (London) NATUAS 0028-0836 441, 719 (2006). 10.1038/nature04861
13. J. Lewis, Curr. Biol. 13, 1398 (2003). CUBLE2 0960-9822 10.1016/S0960-9822(03)00534-7
14. M. Doi, Nature Commun. NCAOBW 2041-1723 2, 327 (2011). 10.1038/ncomms1316
15. M. Ukai-Tadenuma, R.G. Yamada, H. Xu, J.A. Ripperger, A.C. Liu, and H.R. Ueda, Cell 144, 268 (2011). CELLB5 0092-8674 10.1016/j.cell.2010.12.019
16. P.R. Roelfsema, A.K. Engel, P. König, and W. Singer, Nature (London) NATUAS 0028-0836 385, 157 (1997). 10.1038/385157a0
17. A.T. Winfree, J. Theor. Biol. 16, 15 (1967). JTBIAP 0022-5193 10.1016/0022-5193(67)90051-3
18. B. Ermentrout, Neural Comput. 8, 979 (1996). NEUCEB 0899-7667 10.1162/neco.1996.8.5.979
19. F.C. Hopendsteadt and E.M. Izhikevich, Weakly Connected Neural Networks (Springer, New York, 1997).
20. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, New York, 1984).
21. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, England, 2001).
22. E.M. Izhikevich, Phys. Rev. E PLEEE8 1063-651X 58, 905 (1998). 10.1103/PhysRevE.58.905
23. D. Golomb, D. Hansel, B. Shraiman, and H. Sompolinsky, Phys. Rev. A 45, 3516 (1992). PLRAAN 1050-2947 10.1103/PhysRevA.45.3516
24. A. Halanay, Differential Equations; Stability, Oscillations, Time Lags (Academic Press, New York, 1966).
25. J. Hale, Theory of Functional Differential Equations (Springer-Verlag., Berlin, 1977).
26. C. Simmendinger, A. Wunderlin, and A. Pelster, Phys. Rev. E PLEEE8 1063-651X 59, 5344 (1999). 10.1103/PhysRevE.59.5344
27. L.P. Shayer and S.A. Campbell, SIAM J. Appl. Math. 61, 673 (2000). SMJMAP 0036-1399 10.1137/S0036139998344015