Abstract
To study the effect of parameter mismatch on the stability in a general fashion, we derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. We define master stability equations and associated master stability functions, which are independent of the network structure. In particular, we present several examples of coupled near-identical Lorenz systems configured in small networks (a ring graph and sequence networks) with a fixed parameter mismatch and a large Barabasi-Albert scale-free network with random parameter mismatch. We find that several different network architectures permit similar results despite various mismatch patterns. abstract environment.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Lancaster, P., Tismenetsky, M.: The Theory of Matrices with Applications, 2nd edn. Academic Press, London (1985)
Pecora, L.M., Carroll, T.L.: Synchronization in Chaotic Systems. Phys. Rev. Lett. 64, 821 (1990)
Cuomo, K.M., Oppenheim, A.V.O.: Circuit implementation of synchronized chaos with applications to communications. Phys. Rev. Lett. 71, 65 (1993)
Strogatz, S.H., Stewart, I.: Coupled oscillators and biological synchronization. Scientific American 269, 102 (1993)
Rugh, W.J.: Linear System Theory, 2nd edn. Prentice Hall, New Jersey (1996)
Venkataramani, S.C., Hunt, B.R., Ott, E.: Bubbling Transition. Phys. Rev. E 54, 1346 (1996)
Venkataramani, S.C., Hunt, B.R., Ott, E., Gauthier, D.J., Bienfang, J.C.: Transition to Bubbling of Chaotic Systems. Phys. Rev. Lett. 77, 5361 (1996)
Peroca, L.M., Carroll, T.L.: Master Stability Functions for Synchronized Coupled Systems. Phys. Rev. Lett. 80, 2109 (1998)
Barabasi, A.-L., Albert, R.: Emergence of Scaling in Random Networks. Science 286, 509 (1999)
Buono, P.L., Golubitsky, M.: Models of central pattern generators for quadruped locomotion: I. primary gaits. J. Math. Biol. 42, 291 (2001)
Bocccaletti, S., Kurths, J., Osipov, G., Valladares, D.L., Zhou, C.S.: The synchronization of chaotic systems. Phys. Rep. 366, 1 (2002)
Albert, R., Barabasi, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)
Strogatz, S.H.: Sync: The Emerging Science of Spontaneous Order. Hyperion, New York (2003)
He, D., Stone, L.: Spatio-temporal synchronization of recurrent epidemics. Proc. R. Soc. Lond. B 270, 1519 (2003)
Nishikawa, T., Motter, A.E., Lai, Y.-C., Hoppensteadt, F.C.: Heterogeneity in Oscillator Networks: Are Smaller Worlds Easier to Synchronize? Phys. Rev. Lett. 91, 014101 (2003)
Li, X., Chen, G.: Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint. IEEE Trans. on Circ. Syst. 50, 1381 (2003)
Restrepo, J.G., Ott, E., Hunt, B.R.: Spatial patterns of desynchronization bursts in networks. Phys. Rev. E 69, 066215 (2004)
Skufca, J.D., Bollt, E.M.: Communication and Synchronization in Disconnected Networks with Dynamic Topology Moving Neighborhood Networks. Mathematical Biosciences and Engineering 1, 347 (2004)
Stilwell, D.J., Bollt, E.M., Roberson, D.G.: Sufficient Conditions for Fast Switching Synchronization in Time-Varying Network Topologies. SIAM J. Applied Dynamical Systems 5, 140 (2006)
Arenas, A., Diaz-Guilera, A., Perez-Vicente, C.J.: Synchronization Reveals Topological Scales in Complex Networks. Phys. Rev. Lett. 96, 114102 (2006)
Sun, J., Nishikawa, T., ben-Avraham, D.: Sequence Nets. Phys. Rev. E 78, 026104 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
About this paper
Cite this paper
Sun, J., Bollt, E.M., Nishikawa, T. (2009). Synchronization Stability of Coupled Near-Identical Oscillator Network. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02466-5_90
Download citation
DOI: https://doi.org/10.1007/978-3-642-02466-5_90
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02465-8
Online ISBN: 978-3-642-02466-5
eBook Packages: Computer ScienceComputer Science (R0)