Dynamical aspects of interaction networks

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 15, Issue 11, 2005, Pages 3467-3480

  Nicolis, G ^a   Cantú, A García ^a   Nicolis, C ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b ROYAL METEOROLOGICAL INSTITUTE OF BELGIUM   (Belgium)

Author keywords

Coarse graining; Connectivity matrix; Markov partitions; Unstable dynamical systems

Indexed keywords

EID: 32044473945     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127405014167     Document Type: Article

References (13)

1. Albert, R. & Barabasi, A. [2002] "Statistical mechanics of complex networks," Rev. Mod. Phys. 74, 47-97.
2. Balakrishnan, V., Nicolis, G. & Nicolis, C. [1997] "Recurrence time statistics in chaotic dynamics I: Discrete time maps," J. Stat. Phys. 86, 191-212.
3. Gardiner, C. [1983] Handbook of Stochastic Methods (Springer, Berlin), 442 pp.
4. Gaspard, P. & Nicolis, G. [1983] "What can we learn from homoclinic orbits in chaotic dynamics?" J. Stat. Phys. 31, 499-518.
5. Hemmer, P. C. [1984] "The exact invariant density for a cusp-shaped return map," J. Phys. A17, L247-L249.
6. Kaneko, K. [1989] "Pattern dynamics in spatiotemporal chaos," Physica D34, 1-41.
7. Mc Kernan, D. & Nicolis, G. [1994] "Generalized Markov coarse graining and spectral decomposition of chaotic piecewise linear maps," Phys. Rev. E50, 988-999.
8. Nicolis, C. [1998] "Atmospheric analogs and recurrence time statistics: Toward a dynamical formulation," J. Atmos. Sci. 55, 465-475.
9. Nicolis, G., Martinez, S. & Tirapegui, E. [1991] "Finite coarse graining and Chapman Kolmogorov equation in conservative dynamical systems," Chaos Solit. Pract. 1, 25-37.
10. Nicolis, G. [1995] Introduction to Nonlinear Science (Cambridge University Press, Cambridge), 254 pp.
11. Rössler, O. [1979] "Continuous chaos - four prototype equations," Ann. N. Y. Acad. Sci. 316, 376-392.
12. Shilnikov, L. P. [1965] "A case of existence of denumerable set of periodic motions," Sov. Math. Dokl. 6, 163-166.
13. Thomas, R. [1981] "On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations," Springer Series in Synergetics, Vol. 9 (Springer, Berlin), pp. 80-193.