Guaranteeing global synchronization in networks with stochastic interactions

New Journal of Physics

Volumn 14, Issue , 2012, Pages

  Klinglmayr, Johannes ^a   Kirst, Christoph ^b   Bettstetter, Christian ^a   Timme, Marc ^b  

^a UNIVERSITY OF KLAGENFURT   (Austria)

^b MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY NETWORKS; DELAYED PULSE; DISTRIBUTED SYNCHRONIZATION; ENERGY EFFICIENT; GLOBAL SYNCHRONIZATION; INITIAL CONDITIONS; MOBILE PHONE NETWORKS; PULSE EMISSIONS; RESPONSE FUNCTIONS; STOCHASTIC INTERACTION; SWARM ROBOTS;

ELECTRIC NETWORK TOPOLOGY; SENSOR NETWORKS;

SYNCHRONIZATION;

EID: 84864352598     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/14/7/073031     Document Type: Article

References (36)

1. Strogatz S H 2001 Exploring complex networks Nature 410 268-76 (Pubitemid 32216604)
2. Kinzel W 2008 On the stationary state of a network of inhibitory spiking neurons J. Comput. Neurosci. 24 105-12 (Pubitemid 351148255)
3. Friedrich J and Kinzel W 2009 Dynamics of recurrent neural networks with delayed unreliable synapses: metastable clustering J. Comput. Neurosci. 27 65-80
4. Kirst C, Geisel T and Timme M 2009 Sequential desynchronization in networks of spiking neurons with partial reset Phys. Rev. Lett. 102 068101
5. Hammond C, Bergman H and Brown P 2007 Pathological synchronization in Parkinson's disease: networks, models and treatments Trends Neurosci. 30 357-64 (Pubitemid 46994777)
6. Popovych O V, Hauptmann C and Tass P A 2005 Effective desynchronization by nonlinear delayed feedback Phys. Rev. Lett. 94 164102
7. Mormann F, Andrzejak R G, Kreuz T, Rieke C, David P, Elger C E and Lehnertz K 2003 Automated detection of a preseizure state based on a decrease in synchronization in intracranial electroencephalogram recordings from epilepsy patients Phys. Rev. E 67 021912
8. Peskin C S 1975 Mathematical aspects of heart physiology Courant Institute Lecture Notes (New York: Courant Institute of Mathematical Sciences)
9. Hicke K, D'Huys O, Flunkert V, Schöll E, Danckaert J and Fischer I 2011 Mismatch and synchronization: influence of asymmetries in systems of two delay-coupled lasers Phys. Rev. E 83 056211
10. Blaabjerg F, Teodorescu R, Liserre M and Timbus A V 2006 Overview of control and grid synchronization for distributed power generation systems IEEE Trans. Ind. Electron. 53 1398-409 (Pubitemid 44593490)
11. Bregni S 2002 Synchronization of Digital Telecommunications Networks (New York: Wiley)
12. Tyrrell A, Auer G and Bettstetter C 2010 Emergent slot synchronization in wireless networks IEEE T. Mobile Comput. 9 719-32
13. Mathar R and Mattfeldt J 1996 Pulse-coupled decentral synchronization SIAM J. Appl. Math. 56 1094-106 (Pubitemid 126551904)
14. Hong Y-W and Scaglione A 2005 A scalable synchronization protocol for large scale sensor networks and its applications IEEE J. Sel. Areas Commun. 23 1085-99 (Pubitemid 40730050)
15. Pagliari R and Scaglione A 2011 Scalable network synchronization with pulse-coupled oscillators IEEE T. Mobile Comput. 10 392-405
16. Kuramoto Y 1984 Chemical Oscillations, Waves and Turbulence (Berlin: Springer)
17. Canale E and Monzón P 2008 Almost global synchronization of symmetric Kuramoto coupled oscillators Systems Structure and Control ed P Husek (Rijeka, Croatia: InTech) pp 167-90
18. Mirollo R E and Strogatz S H 1990 Synchronization of pulse-coupled biological oscillators SIAM J. Appl. Math. 50 1645-62
19. Ernst U, Pawelzik K and Geisel T 1995 Synchronization induced by temporal delays in pulse-coupled oscillators Phys. Rev. Lett. 74 1570-3
20. Ernst U, Pawelzik K and Geisel T 1998 Delay-induced multistable synchronization of biological oscillators Phys. Rev. E 57 2150-62
21. Brunel N 2000 Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons J. Comput. Neurosci. 8 183-208 (Pubitemid 30219050)
22. Klinglmayr J, Bettstetter C and Timme M 2009 Globally stable synchronization by inhibitory pulse coupling Proc. Int. Symp. on Applied Science in Biomedical and Communication Technologies (ISABEL) (Bratislava, Slovak Republic) (Piscataway, NJ: IEEE)
23. Klinglmayr J and Bettstetter C 2010 Synchronization of inhibitory pulse-coupled oscillators in delayed random and line networks Proc. Int. Symp. on Applied Sciences in Biomedical and Communication Technologies (ISABEL) (Rome, Italy) (Piscataway, NJ: IEEE)
24. LaMar M D and Smith G D 2010 Effect of node-degree correlation on synchronization of identical pulse-coupled oscillators Phys. Rev. E 81 046206
25. Klinglmayr J and Bettstetter C 2012 Self-organizing synchronization with inhibitory-coupled oscillators: convergence and robustness ACM Trans. Auton. Adapt. Syst. 7 at press
26. Timme M, Wolf F and Geisel T 2002 Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators Phys. Rev. Lett. 89 258701
27. Timme M and Wolf F 2008 The simplest problem in the collective dynamics of neural networks: is synchrony stable? Nonlinearity 21 1579
28. Memmesheimer R-M and Timme M 2010 Stable and unstable periodic orbits in complex networks of spiking neurons with delays Discr. Cont. Dyn. Syst. 28 1555-88
29. Nishimura J and Friedman E J 2011 Robust convergence in pulse-coupled oscillators with delays Phys. Rev. Lett. 106 194101
30. Watts D J and Strogatz S H 1998 Collective dynamics of small-world networks Nature 393 440-2
31. Goldsmith A 2005 Wireless Communications (Cambridge: Cambridge University Press)
32. Eberspächer J, Vögel H-J, Bettstetter C and Hartmann C 2009 GSM-Architecture, Protocols and Services 3rd edn (Chichester: Wiley)
33. Gardiner C W 1985 Handbook of Stochastic Methods (Berlin: Springer)
34. Lundelius L and Lynch N 1984 An upper and lower bound for clock synchronization Inf. Control 62 190-204 (Pubitemid 15514268)
35. Kopetz H 2003 Real-time Systems: Design Principles for Distributed Embedded Applications (Boston, MA: Kluwer)
36. Steingrube S, Timme M, Wörgötter F and Manoonpong P 2010 Self-organized adaptation of a simple neural circuit enables complex robot behaviour Nature Phys. 6 224