Synchronization of oscillators coupled through an environment

Physica D: Nonlinear Phenomena

Volumn 237, Issue 22, 2008, Pages 2933-2944

  Katriel, Guy ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Biological rhythms; Indirectly coupled oscillators; Synchronization

Indexed keywords

STABILITY CRITERIA;

BIOLOGICAL RHYTHM; COUPLED OSCILLATORS; GONADOTROPIN-RELEASING HORMONE; HYPOTHALAMIC NEURON; SYNCHRONIZED OSCILLATIONS; WEAK COUPLINGS;

SYNCHRONIZATION;

EID: 53249092269     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2008.04.015     Document Type: Article

References (28)

1. Camacho E., Rand R., and Howland H. Dynamics of two van der Pol oscillators coupled via a bath. Internat. J. Solids Structures 41 (2004) 2133-2143
2. Foster R., and Kreitzman B. Rhythms of Life (2004), Profile Books, London
3. Furusawa C., and Kaneko K. Emergence of rules in cell society: differentiation, hierarchy and stability. Bull. Math. Biol. 60 (1998) 659-687
4. Garcia-Ojalvo J., Elowitz M.B., and Strogatz S.H. Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing. PNAS 27 (2004) 10955-10960
5. Geier F., Becker-Weimann S., Kramer A., and Herzel H. Entrainment in a model of the mamalian circadian oscillator. J. Biol. Rhythms 20 (2005) 83-93
6. Glass L., and Mackey M.C. From Clocks to Chaos: The Rhythms of Life (1988), Princeton U. Press, Princeton
7. Goldbeter A. Biochemical Oscillations and Cellular Rhythms (1996), Cambridge U. Press, Cambridge
8. Gonze D., Bernard S., Waltermann C., Kramer A., and Herzel H. Spontaneous synchronization of coupled circadian oscillators. Biophys. J. 89 (2005) 120-129
9. Henson M.A. Modeling the synchronization of yeast respiratory oscillations. J. Theoret. Biol. 231 (2004) 443-458
10. Hess B. Periodic patterns in biochemical reactions. Quart. Rev. Biophys. 30 (1997) 121-176
11. Hoppensteadt F.C., and Izhikevich E.M. Weakly Connected Neural Networks (1997), Springer Verlag, New-York
12. Hoppensteadt F.C., and Keener J.P. Phase locking of biological clocks. J. Math. Biol. 15 (1982) 339-349
13. Kato T. Perturbation Theory for Linear Operators (1995), Springer-Verlag, Berlin
14. Khadra A., and Li Y.X. A model for the pulsatile secretion of gonadotropin-releasing hormone from synchronized hypothalamic neurons. Biophys. J. 91 (2006) 74-83
15. Kruse K., and Jülicher F. Oscillations in cell biology. Curr. Opin. Cell Bio. 17 (2005) 20-26
16. Kuznetsov A., Kærn M., and Kopell N. Synchrony in a population of hysteresis-based genetic oscillators. SIAM J. Appl. Math. 65 (2005) 392-425
17. Madsen M.F., Danø S., and Sørensen P.G. On the mechanisms of glycolytic oscillations in yeast. FEBS Journal 272 (2005) 2648-2660
18. Manrubia S.C., Mikhailov A.S., and Zanette D.H. Emergence of Dynamical Order (2004), World Scietific, New-Jersey
19. Pikovsky A., Rosenblum M., and Kurths J. Synchronization: A Universal Concept in Nonlinear Sciences (2001), Cambridge University Press, Cambridge
20. Robinson C. Dynamical Systems (1995), CRC Press, Boca Raton
21. Schibler U., and Naef F. Cellular oscillators: Rhythmic gene expression and metabolism. Current Opinion Cell Biol. 15 (2005) 223-229
22. Toth R., Taylor A.F., and Tinsley M.R. Collective behavior of a population of chemically coupled oscillators. J. Phys. Chem. B 110 (2006) 10170-10176
23. Wang R., and Chen L. Synchronizing genetic oscillators by signalling molecules. J. Biol. Rhythms 20 (2005) 257-269
24. Watanabe M. Bifurcation of synchronized periodic solutions in systems of coupled oscillators I: Perturbation results for weak and strong coupling. Rocky Mountain J. Math 23 (1993) 1483-1525
25. Winfree A.T. The Geometry of Biological Time (2001), Springer, New-York
26. Wolf J., and Heinrich R. Dynamics of two-component biochemical systems in interacting cells; Synchronization and desynchronization of oscillations and multiple steady states. BioSystems 43 (1997) 1-24
27. Wolf J., and Heinrich R. Effect of cellular interaction on glycolytic oscillations in yeast: A theoretical investigation. Biochem J. 345 (2000) 321-334
28. Zhdanov V.P., and Kasemo B. Synchronization of metabolic oscillations: Two cells and ensembles of adsorbed cells. J. Biochem. Phys. 27 (2001) 295-311