Partial synchronization in coupled chemical chaotic oscillators

Journal of Computational and Applied Mathematics

Volumn 233, Issue 8, 2010, Pages 1897-1904

  Wang, Jun Wei ^a   Chen, Ai Min ^b  

^a GUANGDONG UNIVERSITY OF FOREIGN STUDIES   (China)

^b HENAN UNIVERSITY   (China)

Author keywords

Chemical chaos; Clustering; Linear invariant manifold; Nonlinear contraction principle; Partial synchronization

Indexed keywords

ANALYTICAL METHOD; CHAOTIC OSCILLATORS; CHEMICAL OSCILLATORS; CHEMICAL SYSTEMS; DYNAMICAL PROPERTIES; EXPONENTIAL STABILITY; FLUX BOUNDARY CONDITIONS; GLOBAL STATE; GLOBAL SYNCHRONIZATION; INVARIANT MANIFOLDS; LINEAR INVARIANT MANIFOLD; PARTIAL SYNCHRONIZATION; SUFFICIENT CONDITIONS; UNIFORM PHASE;

CIRCUIT OSCILLATIONS; NONLINEAR CONTROL SYSTEMS; NUMERICAL METHODS; SHRINKAGE; SYNCHRONIZATION;

CHEMICAL STABILITY;

EID: 70450235264     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2009.09.026     Document Type: Article

References (38)

1. Torre V. A theory of synchronization of heart pacemaker cells. J. Theoret. Biol. 61 (1976) 55-71
2. Perc M. Stochastic resonance on excitable small-world networks via a pacemaker. Phys. Rev. E 76 (2007) 066203
3. Perc M. Stochastic resonance on weakly paced scale-free networks. Phys. Rev. E 78 (2008) 036105
4. Winfree A.T. The Geometry of Biological Time (1980), Springer, New York
5. Yamaguchi S., Isejima H., Matsuo T., Okura R., Yagita K., Kobayashi M., and Okamura H. Synchronization of cellular clocks in the suprachiasmatic nucleus. Science 302 (2003) 1408-1412
6. Kiss I.Z., Zhai Y.M., and Hudson J.L. Emerging coherence in a population of chemical oscillators. Science 296 (2002) 1676-1678
7. Kiss I.Z., Zhai Y., and Hudson J.L. Collective dynamics of chaotic chemical oscillators and the law of large numbers. Phys. Rev. Lett. 88 (2002) 238301
8. Wiesenfeld K., and Swift J.W. Averaged equations for Josephson junction series arrays. Phys. Rev. E 51 (1995) 1020-1025
9. C.H. Huygens, Horoloqium Oscillatorium, Parisiis, France, 1673
10. Pikovsky A., Rosenblum M., and Kurths J. Synchronization: A Universal Concept in Nonlinear Sciences (2001), Cambridge University Press
11. Pecora L.M., and Carroll T.L. Synchronization in chaotic systems. Phys. Rev. Lett. 64 (1990) 821-826
12. Boccaletti S., Kurths J., Osipov G., Valladares D.L., and Zhou C.S. The synchronization of chaotic systems. Phys. Rep. 366 (2002) 1-101
13. Belykh V., Belykh I., and Mosekilde E. Cluster synchronization modes in an ensemble of coupled chaotic oscillators. Phys. Rev. E 63 (2001) 036216
14. Belykh I., Belykh V., Nevidin K., and Hasler M. Persistent clusters in lattices of coupled nonidentical chaotic systems. Chaos 13 (2003) 165-178
15. Pyragas K. Weak and strong synchronization of chaos. Phys. Rev. E 54 (1996) 4508-4511
16. Wang J.W., Zhang J.J., Yuan Z.J., Chen A.M., and Zhou T.S. Neurotransmitter-mediated collective rhythms in grouped Drosophila circadian clocks. J. Biol. Rhythms 23 (2008) 472-482
17. Pham Q.C., and Slotine J.J. Stable concurrent synchronization in dynamic system networks. Neural Netw. 20 (2006) 62-77
18. M. Golubitsky, I. Stewart, Synchrony versus symmetry in coupled cells, in: Equadiff 2003: Proceedings of the International Conference on Differential Equations
19. Kaneko K. Relevance of dynamic clustering to biological networks. Physica D 75 (1994) 55-73
20. Rulkov N.F. Images of synchronized chaos: Experiments with circuits. Chaos 6 (1996) 262-279
21. Belykh I., Belykh V., and Hasler M. Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems. Phys. Rev. E 62 (2000) 6332-6345
22. Yanchuk S., Maistrenko Y., and Mosekilde E. Partial synchronization and clustering in a system of diffusively coupled chaotic oscillators. Math. Comp. Simul. 54 (2001) 491-508
23. Banaji M. Clustering in globally coupled oscillators. Dyn. Syst. 17 (2002) 263-285
24. Pogromsky A.Y., Santoboni G., and Nijmeijer H. Partial synchronization: From symmetry towards stability. Physica D 172 (2002) 65-87
25. Qin W.X., and Chen G.R. Coupling schemes for cluster synchronization in coupled Josephson equations. Physica D 197 (2004) 375-391
26. Ma Z.J., Liu Z.R., and Zhang G. A new method to realize cluster synchronization in connected chaotic networks. Chaos 16 (2006) 023103
27. Belykh V., Belykh I., Hasler M., and Nevidin K. Cluster synchronization in three-dimensional lattices of diffusively coupled oscillators. Int. J. Bifurcat. Chaos 13 (2003) 755-779
28. Blasius B., and Stone L. Chaos and phase synchronization in ecological systems. Int. J. Bifurcat. Chaos 11 (2000) 2361-2380
29. Wolf A., Swift J.B., Swinney H.L., and Vastano J.A. Determining Lyapunov exponents from a time series. Physica D 16 (1985) 285-317
30. Samardzija N., Greller L.D., and Wasserman E. Nonlinear chemical kinetic schemes derived from mechanical and electrical dynamical systems. J. Chem. Phys. 90 (1989) 2296-2304
31. Rossler O.E. An equation for continuous chaos. Phys. Lett. A 57 (1976) 397-398
32. Güémez J., and Matias M.A. Intrinsic-noise-induced transitions in chaotic systems. Phys. Rev. E 51 (1995) 3059-3068
33. Wang M.S., Hou Z.H., and Xin H.W. Internal noise-enhanced phase synchronization of coupled chemical chaotic oscillators. J. Phys. A: Math. Gen. 38 (2005) 145-152
34. Heagy J.F., Pecora L.M., and Carroll T.L. Short wavelength bifurcations and size instabilities in coupled oscillator systems. Phys. Rev. Lett. 74 (1995) 4185-4188
35. Lohmiller W., and Slotine J.J. On contraction analysis for nonlinear systems. Automatica 34 (1998) 683-696
36. Wang W., and Slotine J.J. On partial contraction analysis for coupled nonlinear oscillators. Biol. Cybern. 92 (2005) 38-53
37. Horn R., and Johnson C. Matrix Analysis (1985), Cambridge University Press
38. A. Jadbabaie, N. Motee, M. Barahona, On the stability of the Kuramoto model of coupled nonlinear oscillators, in: Proceedings of the American Control Conf., 2004