Distributed Delays Facilitate Amplitude Death of Coupled Oscillators

Physical Review Letters

Volumn 91, Issue 9, 2003, Pages

  Atay, Fatihcan M ^a  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL MODEL; BIOLOGICAL RHYTHM; HEART ARRHYTHMIA; MEMORY; PERIODICITY;

ARRHYTHMIAS, CARDIAC; BIOLOGICAL CLOCKS; MEMORY; MODELS, BIOLOGICAL; MODELS, NEUROLOGICAL; PERIODICITY;

BIFURCATION (MATHEMATICS); MATHEMATICAL MODELS; OSCILLATIONS; SYSTEM STABILITY;

DISTRIBUTED DELAYS;

LARGE SCALE SYSTEMS;

EID: 9744234606     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.91.094101     Document Type: Article

References (31)

1. D.A. Linkens, Bull. Math. Biol. 39, 359 (1977);
2. S. Daan and C. Berde, J. Theor. Biol.00225193 70, 297 (1978);
3. P. Hadley, M.R. Beasley, and K. Wiesenfeld, Phys. Rev. B10.1103/PhysRevB.38.8712 38, 8712 (1988);
4. M. Kawato and R. Suzuki, J. Theor. Biol. 86, 547 (1980);
5. A.T. Winfree, The Geometry of Biological Time (Springer, New York, 1980);
6. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984);
7. J. Benford, H. Sze, W. Woo, R.R. Smith, and B. Harteneck, Phys. Rev. Lett.10.1103/PhysRevLett.62.969 62, 969 (1989);
8. M.F. Crowley and I.R. Epstein, J. Phys. Chem. 93, 2496 (1989);
9. J.D. Murray, Mathematical Biology (Springer, New York, Berlin, Heidelberg, 1993), 2nd ed.;
10. M. Dolnik and I.R. Epstein, Phys. Rev. EPLEEE810.1103/PhysRevE.54.3361 54, 3361 (1996);
11. P.M. Varangis, A. Gavrielides, T. Erneux, V. Kovanis, and L.F. Lester, Phys. Rev. Lett.10.1103/PhysRevLett.78.2353 78, 2353 (1997);
12. T.D. Frank, A. Daffertshofer, C.E. Peper, P.J. Beeka, and H. Haken, Physica (Amsterdam) 144D, 62 (2000).
13. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization—A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, 2001).
14. Y. Yamaguchi and H. Shimizu, Physica (Amsterdam)10.1016/0167-2789(84)90444-5 11D, 212 (1984).
15. K. Bar-Eli, Physica (Amsterdam)10.1016/0167-2789(85)90182-4 14D, 242 (1985).
16. D.G. Aronson, G.B. Ermentrout, and N. Kopell, Physica (Amsterdam)10.1016/0167-2789(90)90007-C 41D, 403 (1990).
17. G.B. Ermentrout, Physica (Amsterdam)10.1016/0167-2789(90)90124-8 41D, 219 (1990).
18. R.E. Mirollo and S.H. Strogatz, J. Stat. Phys. 60, 245 (1990).
19. D.V. Ramana Reddy, A. Sen, and G.L. Johnston, Phys. Rev. Lett.10.1103/PhysRevLett.80.5109 80, 5109 (1998);
20. D.V. Ramana ReddyA. SenG.L. JohnstonPhysica (Amsterdam)10.1016/S0167-2789(99)00004-4 129D, 15 (1999).
21. R. Herrero, M. Figueras, J. Rius, F. Pi, and G. Orriols, Phys. Rev. Lett.10.1103/PhysRevLett.84.5312 84, 5312 (2000).
22. D.V. Ramana Reddy, A. Sen, and G.L. Johnston, Phys. Rev. Lett.10.1103/PhysRevLett.85.3381 85, 3381 (2000).
23. F.M. Atay, Physica (Amsterdam) 183D, 1–18 (2003).
24. V. Volterra, Lecons sur la théorie mathématique de la lutte pour la vie (Gauthiers-Villars, Paris, 1931).
25. N. MacDonald, Time Lags in Biological Models, Lecture Notes in Biomathematics Vol.�27 (Springer, Berlin, 1978).
26. R.M. May, Stability and Complexity in Model Ecosystems (Princeton University Press, Princeton, NJ, 1974).
27. K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics (Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992).
28. D.A. Baylor, A.L. Hodgkin, and T.D. Lamb, J. Physiol. (London)JPHYA7 242, 685 (1974).
29. A.D. Drozdov and V.B. Kolmanovskii, Stability in Viscoelasticity (North-Holland, Amsterdam, 1994).
30. J.B.S. Haldane, Rev. Econ. Stud. 1, 186 (1933).
31. J.M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathematics Vol.�20 (Springer-Verlag, New York, 1977).