New approach to synchronization analysis of linearly coupled ordinary differential systems

Physica D: Nonlinear Phenomena

Volumn 213, Issue 2, 2006, Pages 214-230

  Lu, Wenlian ^a,b   Chen, Tianping ^a  

^a FUDAN UNIVERSITY   (China)

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

Author keywords

Linearly coupled ordinary differential systems; Stability of synchronization manifold; Synchronization manifold; Transverse space

Indexed keywords

CHAOS THEORY; EIGENVALUES AND EIGENFUNCTIONS; LINEAR SYSTEMS; MATRIX ALGEBRA; SYNCHRONIZATION; SYSTEM STABILITY;

LINEARLY COUPLED ORDINARY DIFFERENTIAL EQUATIONS (LCODE); STABILITY OF SYNCHRONIZATION MANIFOLD; SYNCHRONIZATION MANIFOLD; TRANSVERSE SPACE;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 30144443190     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2005.11.009     Document Type: Article

References (36)

1. A.T. Winfree The Geometry of Biological Time 1980 Springer Verlag New York
2. A. Turing The chemical basis of morphogenesis Phil. Trans. R. Soc. B 237 1952 37
3. Y. Kuramoto Chemical Oscillations, Waves, and Turbulence 1984 Springer-Verlag New York
4. M. Dhamala, V.K. Jirsa, and M. Ding Transitions to synchrony in coupled bursting neurons Phys. Rev. Lett. 92 2 2004 028101-1
5. A.L. Lloyd, and V.A.A. Jansen Spatiotemporal dynamics of epidemics: synchrony in metapopular models Math. Biosci. 188 2004 1 16
6. L.M. Pecora, and T.L. Carroll Synchronization in chaotic systems Phys. Rev. Lett. 64 8 1990 821 824
7. R.E. Mirollo, and S.H. Strogatz Synchronization properties of pulse-coupled biological oscillators SIAM J. Appl. Math. 50 1990 1645 1662
8. J.F. Heagy, T.L. Carroll, and L.M. Pecora Synchronous chaos in coupled oscillator systems Phys. Rev. E 50 1994 1874 1885
9. M. Lashmanan, and K. Murali Chaos in Nonlinear Oscillator: Controlling and Synchronization 1996 World Scientific Singapore
10. C. Huygens Horoloquim Oscillatorium 1672 F. Muguet. Paris
11. L. Kunbert, K.I. Agladze, and V.I. Krinsky Image processing using light-sensitive chemical waves Nature 337 1989 244 247
12. V.I. Krinsky, V.N. Biktashev, and I.R. Efimov Autowaves principles for parallel image processing Physica D 49 1991 247 253
13. V. Perez-Manuzuri, V. Perez-Villar, and L.O. Chua Autowaves for image processing on a two-dimensional CNN array of excitable nonlinear circuits: flat and wrinkled labyrinths IEEE Trans. Circuits Syst. I 40 1995 174 181
14. W.L. Lu, and T.P. Chen Synchronization of coupled connected neural networks with delays IEEE Trans. CAS-1 51 12 2004 2491 2503
15. G.D. VanWiggeren, and P. Roy Communication with chaotic laser Science 279 20 1998 1198 1200
16. F.C. Hoppensteadt, and E.M. Lzhikevich Pattern recognition via synchronization in phase-locked loop neural networks IEEE Trans. Neural Netw. 11 3 2000 734 738
17. L.M. Pecora, T. Carroll, G. Johnson, D. Mar, and K.S. Fink Synchronization stability in coupled oscillator arrays: solution for arbitrary configuration Internat. J. Bifur. Chaos 10 2 2000 273 290
18. X.F. Wang, and G. Chen Synchronization in scale-free dynamical networks: robustness and fragility IEEE Trans. Circuits Syst. I 49 1 2002 54 62
19. C.W. Wu, and L.O. Chua Synchronization in an array of linearly coupled dynamical systems IEEE Trans. Circuits Syst. I 42 8 1995 430 447
20. C.W. Wu Synchronization in networks of nonlinear dynamical systems coupled via a directed graph Nonlinearity 18 2005 1057 1064
21. X.F. Wang, and G. Chen Synchronization small-world dynamical networks Internat. J. Bifur. Chaos 12 1 2002 187 192
22. P.A. Horn, and C.R. Johnson Matrix Analysis' 1985 Cambridge University Press New York
23. H. Minc Nonnegative Matrices 1988 Wiley New York
24. A. Baciotti, R. Conti, and P. Marcellini Discontinuous Ordinary Differential Equations and Stabilization 2000 Universita di Firenze
25. F.H. Clarke Optimization and Nonsmooth Analysis 1983 Wiley and Sons New York
26. Y. Chen, G. Rangarajan, and M. Ding General stability analysis of synchronized dynamics in coupled systems Phys. Rev. E. 67 2003 026209
27. P. Ashwin, J. Buescu, and I. Stewart From attractor to chaotic saddle, a tale of transverse instability Nonlinearity 9 1996 703 737
28. J.C. Alexander, I. Kan, J.A. Yorke, and Z. You Saddled basins Internat. J. Bifur. Chaos 2 1992 795 813
29. G. Chen, J. Zhou, and Z. Liu Global synchronization of coupled delayed neural networks with application to chaotic CNN models Internat. J. Bifur. Chaos 14 2004 2229 2249
30. F. Zou, and J.A. Nosse Bifurcation and chaos in cellular neural networks IEEE Trans. CAS-1 40 3 1993 166 173
31. L.O. Chua, and L. Yang Cellular neural networks: Theory IEEE Trans. Circuits Syst. 35 1988 1257 1272
32. L.O. Chua, and L. Yang Cellular neural networks: Applications IEEE Trans. Circuits Syst. 35 1988 1273 1290
33. Y. Zhang, and Z. He A secure communication scheme based on cellular neural networks IEEE Int. Conf. Intell. Process. Systems 1 1997 521 524
34. D.J. Watts, and S.H. Strogatz Collective dynamics of 'small-world' networks Nature 391 4 1998 440 442
35. M.E.J. Newman, and D.J. Watts Renormalization group analysis of the small-world network model Phys. Lett. A 263 9 1999 341 346
36. A.-L. Barabasi, and R. Albert Emergence of scaling in random networks Science 286 15 1999 509 512