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Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 84, Issue 3, 2011, Pages

Coarse graining the dynamics of heterogeneous oscillators in networks with spectral gaps

(2) Rajendran, Karthikeyan a Kevrekidis, Ioannis G a,b

a Princeton University (United States)

b PRINCETON UNIVERSITY (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COARSE GRAINING; COARSE-GRAINED; COMPUTATIONAL TASK; COMPUTER ASSISTED; COUPLING NETWORK; EQUATION-FREE; EVOLUTIONARY DYNAMICS; GRAPH DYNAMICS; INTRINSIC PROPERTY; LAPLACIANS; LIMIT-CYCLE; LOW DIMENSIONAL; NETWORK STRUCTURES; SPECTRAL GAP; UNCERTAINTY QUANTIFICATIONS; NON-IDENTICAL OSCILLATORS; PROJECTIVE INTEGRATIONS;

LAPLACE TRANSFORMS; DYNAMICS;

DYNAMICS; COMPLEX NETWORKS;

EID: 80053110649 PISSN: 15393755 EISSN: 15502376 Source Type: Journal
DOI: 10.1103/PhysRevE.84.036708 Document Type: Article

Times cited : (14)

References (33)

1
- 0003886783
- Springer, Berlin
- Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
- (1984) Chemical Oscillations, Waves, and Turbulence
- Kuramoto, Y.¹

2
- 18844380483
- Computer simulation of a central pattern generator via Kuramoto model
- DOI 10.1016/j.physa.2004.12.046, PII S0378437104016280
- F. A. O. Cruz and C. M. Cortez, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.12.046 353, 258 (2005). (Pubitemid 40684301)
- (2005) Physica A: Statistical Mechanics and its Applications , vol.353 , Issue.1-4 , pp. 258-270
- Cruz, F.A.O.¹ Cortez, C.M.²

3
- 0014108715
- JTBIAP 0022-5193 10.1016/0022-5193(67)90051-3
- A. T. Winfree, J. Theor. Biol. JTBIAP 0022-5193 10.1016/0022-5193(67) 90051-3 16, 15 (1967).
- (1967) J. Theor. Biol. , vol.16 , pp. 15
- Winfree, A.T.¹

4
- 0001164475
- SCIEAS 0036-8075 10.1126/science.254.5039.1750
- G. Ertl, Science SCIEAS 0036-8075 10.1126/science.254.5039.1750 254, 1750 (1991).
- (1991) Science , vol.254 , pp. 1750
- Ertl, G.¹

5
- 0001006240
- PRLTAO 0031-9007 10.1103/PhysRevLett.76.404
- K. Wiesenfeld, P. Colet, and S. H. Strogatz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.404 76, 404 (1996).
- (1996) Phys. Rev. Lett. , vol.76 , pp. 404
- Wiesenfeld, K.¹ Colet, P.² Strogatz, S.H.³

6
- 0039806342
- The sound of many hands clapping
- DOI 10.1038/35002660
- Z. Néda, E. Ravasz, Y. Brechet, T. Vicsek, and A. L. Barabási, Nature (London) NATUAS 0028-0836 10.1038/35002660 403, 849 (2000). (Pubitemid 30130975)
- (2000) Nature , vol.403 , Issue.6772 , pp. 849-850
- Neda, Z.¹ Ravasz, E.² Brechet, Y.³ Vicsek, T.⁴ Barabasi, A.-L.⁵

7
- 19944385353
- The Kuramoto model: A simple paradigm for synchronization phenomena
- DOI 10.1103/RevModPhys.77.137
- J. A. Acebrón, L. L. Bonilla, C. J. Pérez Vicente, F. Ritort, and R. Spigler, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.77. 137 77, 137 (2005). (Pubitemid 41490657)
- (2005) Reviews of Modern Physics , vol.77 , Issue.1 , pp. 137-185
- Acebron, J.A.¹ Bonilla, L.L.² Vicente, C.J.P.³ Ritort, F.⁴ Spigler, R.⁵

8
- 67650096320
- PDNPDT 0167-2789 10.1016/j.physd.2009.04.012
- C. R. Laing, Physica D PDNPDT 0167-2789 10.1016/j.physd.2009.04.012 238, 1569 (2009).
- (2009) Physica D , vol.238 , pp. 1569
- Laing, C.R.¹

9
- 33846607194
- Generalising the Kuramoto model for the study of neuronal synchronisation in the brain
- DOI 10.1016/j.physd.2006.12.004, PII S0167278906004805
- D. Cumin and C. Unsworth, Physica D PDNPDT 0167-2789 10.1016/j.physd. 2006.12.004 226, 181 (2007). (Pubitemid 46185616)
- (2007) Physica D: Nonlinear Phenomena , vol.226 , Issue.2 , pp. 181-196
- Cumin, D.¹ Unsworth, C.P.²

10
- 56549084695
- PRPLCM 0370-1573 10.1016/j.physrep.2008.09.002
- A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2008.09.002 469, 93 (2008).
- (2008) Phys. Rep. , vol.469 , pp. 93
- Arenas, A.¹ Díaz-Guilera, A.² Kurths, J.³ Moreno, Y.⁴ Zhou, C.⁵

11
- 37549062157
- Synchronization of Kuramoto oscillators in random complex networks
- DOI 10.1016/j.physa.2007.11.008, PII S0378437107012071
- P. Li and Z. Yi, Physica A PHYADX 0378-4371 10.1016/j.physa.2007.11.008 387, 1669 (2008). (Pubitemid 50014588)
- (2008) Physica A: Statistical Mechanics and its Applications , vol.387 , Issue.7 , pp. 1669-1674
- Li, P.¹ Yi, Z.²

12
- 67349158301
- PDNPDT 0167-2789 10.1016/j.physd.2009.04.002
- F. Mori and T. Odagaki, Physica D PDNPDT 0167-2789 10.1016/j.physd.2009. 04.002 238, 1180 (2009).
- (2009) Physica D , vol.238 , pp. 1180
- Mori, F.¹ Odagaki, T.²

13
- 85128858890
- I. G. Kevrekidis, C. W. Gear, J. M. Hyman, P. G. Kevrekidis, O. Runborg, and C. Theodoropoulos, Commun. Math. Sci. 1, 715 (2003).
- (2003) Commun. Math. Sci. , vol.1 , pp. 715
- Kevrekidis, I.G.¹ Gear, C.W.² Hyman, J.M.³ Kevrekidis, P.G.⁴ Runborg, O.⁵ Theodoropoulos, C.⁶

14
- 0032482432
- Collective dynamics of 'small-world' networks
- DOI 10.1038/30918
- D. J. Watts and S. H. Strogatz, Nature (London) NATUAS 0028-0836 10.1038/30918 393, 440 (1998). (Pubitemid 28292183)
- (1998) Nature , vol.393 , Issue.6684 , pp. 440-442
- Watts, D.J.¹ Strogatz, S.H.²

15
- 3042720018
- Equation-free: The computer-aided analysis of complex multiscale systems
- DOI 10.1002/aic.10106
- I. G. Kevrekidis, C. W. Gear, and G. Hummer, AIChE J. AICEAC 0001-1541 10.1002/aic.10106 50, 1346 (2004). (Pubitemid 38856761)
- (2004) AIChE Journal , vol.50 , Issue.7 , pp. 1346-1355
- Kevrekidis, I.G.¹ Gear, C.W.² Hummer, G.³

16
- 33749468596
- Finding community structure in networks using the eigenvectors of matrices
- DOI 10.1103/PhysRevE.74.036104
- M. E. J. Newman, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.74.036104 74, 036104 (2006). (Pubitemid 44521558)
- (2006) Physical Review E - Statistical, Nonlinear, and Soft Matter Physics , vol.74 , Issue.3 , pp. 036104
- Newman, M.E.J.¹

17
- 33745342032
- Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
- DOI 10.1016/j.acha.2005.07.004, PII S1063520306000534
- B. Nadler, S. Lafon, R. R. Coifman, and I. G. Kevrekidis, Appl. Comput. Harmon. Anal. AICEAC 1063-5203 10.1016/j.acha.2005.07.004 21, 113 (2006). (Pubitemid 43947618)
- (2006) Applied and Computational Harmonic Analysis , vol.21 , Issue.1 , pp. 113-127
- Nadler, B.¹ Lafon, S.² Coifman, R.R.³ Kevrekidis, I.G.⁴

18
- 43049125805
- Spectral coarse graining and synchronization in oscillator networks
- DOI 10.1103/PhysRevLett.100.174104
- D. Gfeller and P. De Los Rios, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.174104 100, 174104 (2008). (Pubitemid 351624654)
- (2008) Physical Review Letters , vol.100 , Issue.17 , pp. 174104
- Gfeller, D.¹ De Los Rios, P.²

19
- 33645156787
- PRLTAO 0031-9007 10.1103/PhysRevLett.96.114102
- A. Arenas, A. Díaz-Guilera, and C. J. Pérez-Vicente, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.114102 96, 114102 (2006).
- (2006) Phys. Rev. Lett. , vol.96 , pp. 114102
- Arenas, A.¹ Díaz-Guilera, A.² Pérez-Vicente, C.J.³

20
- 33751016333
- Synchronization processes in complex networks
- DOI 10.1016/j.physd.2006.09.029, PII S0167278906003666
- A. Arenas, A. Díaz-Guilera, and C. J. Pérez-Vicente, Physica D PDNPDT 0167-2789 10.1016/j.physd.2006.09.029 224, 27 (2006). (Pubitemid 44751205)
- (2006) Physica D: Nonlinear Phenomena , vol.224 , Issue.1-2 , pp. 27-34
- Arenas, A.¹ Diaz-Guilera, A.² Perez-Vicente, C.J.³

21
- 33847264517
- Analysis of nonlinear synchronization dynamics of oscillator networks by Laplacian spectral methods
- DOI 10.1103/PhysRevE.75.027104
- P. N. McGraw and M. Menzinger, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.027104 75, 027104 (2007). (Pubitemid 46325338)
- (2007) Physical Review E - Statistical, Nonlinear, and Soft Matter Physics , vol.75 , Issue.2 , pp. 027104
- McGraw, P.N.¹ Menzinger, M.²

22
- 40949122707
- Laplacian spectra as a diagnostic tool for network structure and dynamics
- DOI 10.1103/PhysRevE.77.031102
- P. N. McGraw and M. Menzinger, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.031102 77, 031102 (2008). (Pubitemid 351415859)
- (2008) Physical Review E - Statistical, Nonlinear, and Soft Matter Physics , vol.77 , Issue.3 , pp. 031102
- Mcgraw, P.N.¹ Menzinger, M.²

23
- 0000048673
- SIJCD4 0196-5204 10.1137/0907058
- Y. Saad and M. H. Schultz, SIAM J. Sci. Stat. Comput. SIJCD4 0196-5204 10.1137/0907058 7, 856 (1986).
- (1986) SIAM J. Sci. Stat. Comput. , vol.7 , pp. 856
- Saad, Y.¹ Schultz, M.H.²

24
- 0004155392
- SIAM, Philadelphia
- C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, Frontiers in Applied Mathematics no. 16 (SIAM, Philadelphia, 1995).
- (1995) Iterative Methods for Linear and Nonlinear Equations
- Kelley, C.T.¹

25
- 33645794921
- PRLTAO 0031-9007 10.1103/PhysRevLett.96.144101
- S. J. Moon, R. Ghanem, and I. G. Kevrekidis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.144101 96, 144101 (2006).
- (2006) Phys. Rev. Lett. , vol.96 , pp. 144101
- Moon, S.J.¹ Ghanem, R.² Kevrekidis, I.G.³

26
- 70349403807
- NNETEB 0893-6080 10.1016/j.neunet.2009.07.011
- T. Binzegger, R. J. Douglas, and K. A. C. Martin, Neural Netw. NNETEB 0893-6080 10.1016/j.neunet.2009.07.011 22, 1071 (2009).
- (2009) Neural Netw. , vol.22 , pp. 1071
- Binzegger, T.¹ Douglas, R.J.² Martin, K.A.C.³

27
- 84919509027
- Oxford University Press, New York
- C. Laing and G. J. Lord, Stochastic Methods in Neuroscience (Oxford University Press, New York, 2009).
- (2009) Stochastic Methods in Neuroscience
- Laing, C.¹ Lord, G.J.²

28
- 0003519920
- Springer, New York
- R. G. Ghanem and P. D. Spanos, Stochastic Finite Elements: A Spectral Approach (Springer, New York, 1991).
- (1991) Stochastic Finite Elements: A Spectral Approach
- Ghanem, R.G.¹ Spanos, P.D.²

29
- 0037249229
- SJOCE3 1064-8275 10.1137/S1064827501387826
- D. Xiu and G. E. Karniadakis, SIAM J. Sci. Comput. SJOCE3 1064-8275 10.1137/S1064827501387826 24, 619 (2002).
- (2002) SIAM J. Sci. Comput. , vol.24 , pp. 619
- Xiu, D.¹ Karniadakis, G.E.²

30
- 0003851780
- SIAM Publications, Philadelphia
- R. B. Lehoucq, D. C. Sorensen, and C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM Publications, Philadelphia, 1998).
- (1998) ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods
- Lehoucq, R.B.¹ Sorensen, D.C.² Yang, C.³

31
- 48849092313
- CMMECC 0045-7825 10.1016/j.cma.2007.11.033
- G. Samaey, W. Vanroose, D. Roose, and I. G. Kevrekidis, Comput. Methods Appl. Mech. Eng. CMMECC 0045-7825 10.1016/j.cma.2007.11.033 197, 3480 (2008).
- (2008) Comput. Methods Appl. Mech. Eng. , vol.197 , pp. 3480
- Samaey, G.¹ Vanroose, W.² Roose, D.³ Kevrekidis, I.G.⁴

32
- 0346816494
- IECRED 0888-5885 10.1021/ie021062w
- C. I. Siettos, C. C. Pantelides, and I. G. Kevrekidis, Ind. Eng. Chem. Res. IECRED 0888-5885 10.1021/ie021062w 42, 6795 (2003).
- (2003) Ind. Eng. Chem. Res. , vol.42 , pp. 6795
- Siettos, C.I.¹ Pantelides, C.C.² Kevrekidis, I.G.³

33
- 0001639797
- SJOCE3 1064-8275 10.1137/S1064827594277673
- K. Lust and D. Roose, SIAM J. Sci. Comput. SJOCE3 1064-8275 10.1137/S1064827594277673 19, 1188 (1998).
- (1998) SIAM J. Sci. Comput. , vol.19 , pp. 1188
- Lust, K.¹ Roose, D.²

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