Synchronous chaos in coupled map lattices with general connectivity topology

SIAM Journal on Applied Dynamical Systems

Volumn 7, Issue 3, 2008, Pages 755-765

  Juang, Jonq ^a   Liang, Yu Hao ^a  

^a NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

Coupled map lattices; Lyapunov exponents; Stable synchronization; Wavelength bifurcation

Indexed keywords

BIFURCATION (MATHEMATICS); CRYSTAL LATTICES; DIFFERENTIAL EQUATIONS; LYAPUNOV METHODS; MAPS; PROBABILITY DENSITY FUNCTION; TELECOMMUNICATION NETWORKS; TOPOLOGY;

CHAOTIC MAPS; CONVERGENCE RATES; COUPLED MAP LATTICES; COUPLING STRENGTHS; INITIAL VALUES; LYAPUNOV EXPONENTS; NECESSARY AND SUFFICIENT CONDITIONS; NONLINEAR FUNCTIONS; STABILITY FUNCTIONS; STABLE SYNCHRONIZATION; SYNCHRONOUS STATES; TRANSVERSE LYAPUNOV EXPONENTS;

CHAOTIC SYSTEMS;

EID: 55849103482     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/070705179     Document Type: Article

References (34)

1. V. N. BELYKH, N. N. VERICHEV, L. J. KOCAREV, AND L. O. CHUA, Chua's Circuit: A Paradigm for Chaos, World Scientific, Singapore, 1993.
2. V. N. BELYKH, I. V. BELYKH, K. V. NEVIDIN, AND M. HASLER, Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems, Phys. Rev. E (3), 62 (2000), pp. 6332-6345.
3. V. N. BELYKH, I. V. BELYKH, K. V. NEVIDIN, AND M. HASLER, Persistent clusters in lattices of coupled nonidentical chaotic systems, Chaos, 13 (2003), pp. 165-178.
4. V. N. BELYKH, I. V. BELYKH, K. V. NEVIDIN, AND M. HASLER, Cluster synchronization in three-dimensional lattices of diffusively coupled oscillators, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 13 (2003), pp. 755-779.
5. V. N. BELYKH, I. V. BELYKH, AND M. HASLER, Connection graph stability method for synchronized coupled chaotic systems, Phys. D, 195 (2004), pp. 159-187.
6. V. N. BELYKH, I. V. BELYKH, AND M. HASLER, Synchronization in asymmetrically coupled networks with node balance, Chaos, 16 (2006), 015102.
7. J. JUANG, C. L. LI, AND Y. H. LIANG, Global synchronization in lattices of coupled chaotic systems, Chaos, 17 (2007), 033111.
8. L. M. PECORA AND T. L. CARROLL, Master stability functions for synchronized coupled systems, Phys. Rev. Lett., 80 (1998), pp. 2109-2112.
9. A. POGROMSKY AND H. NIJMEIJER, Cooperative oscillatory behavior of mutually coupled dynamical systems, IEEE Trans. Circuits Systems I Fund. Theory Appl., 48 (2001), pp. 152-162.
10. W. WANG AND J.-J. E. SLOTINE, On partial contraction analysis for coupled nonlinear oscillators, Biol. Cybernet., 92 (2005), pp. 38-53.
11. C. W. WU AND L. O. CHUA, Synchronization in an array of linearly coupled dynamical systems, IEEE Trans. Circuits Systems I Fund. Theory Appl., 42 (1995), pp. 430-447.
12. C. W. WU, Cooperative oscillatory behavior of mutually coupled dynamical systems, IEEE Trans. Circuits Systems I Fund. Theory Appl., 48 (2001), pp. 152-162.
13. C. W. WU, Synchronization in coupled arrays of chaotic oscillators with nonreciprocal coupling, IEEE Trans. Circuits Systems I Fund. Theory Appl., 50 (2003), pp. 294-297.
14. C. W. WU, Synchronization in Coupled Chaotic Circuits and Systems, World Scientific Series on Nonlinear Science Series A 41, World Scientific, Singapore, 2002.
15. W.-W. LIN AND Y.-Q. WANG, Chaotic synchronization in coupled map lattices with periodic boundary conditions, SIAM J. Appl. Dyn. Syst., 1 (2002), pp. 175-189.
16. G. HU, J. YANG, AND W. LIU, Instability and controllability of linearly coupled oscillators: Eigenvalue analysis, Phys. Rev. E (3), 58 (1998), pp. 4440-4453.
17. M. ZHAN, G. HU, AND J. YANG, Synchronization of chaos in coupled systems, Phys. Rev. E (3), 62 (2000), pp. 2963-2966.
18. K. S. FINK, G. JOHNSON, T. CARROLL, D. MAR, AND L. PECORA, Three coupled oscillators as a universal probe of synchronization stability in coupled oscillator arrays, Phys. Rev. E (3), 61 (2000), pp. 5080-5090.
19. M. BARAHONA AND L. M. PECORA, Synchronization in small-world systems, Phys. Rev. Lett., 89 (2002), 054101.
20. P. M. GADE AND R. E. AMRITKAR, Spatially periodic orbits in coupled-map lattices, Phys. Rev. E (3), 47 (1993), pp. 143-154.
21. P. M. GADE, H. A. CERDEIRA, AND R. RAMASWAMY, Coupled maps on trees, Phys. Rev. E (3), 52 (1995), pp. 2478-2485.
22. P. M. GADE, Synchronization of oscillators with random nonlocal connectivity, Phys. Rev. E (3), 54 (1996), pp. 64-70.
23. Y. CHEN, G. RANGARAJAN, AND M. DING, General stability analysis of synchronized dynamics in coupled systems, Phys. Rev. E (3), 67 (2003), 026209.
24. D. J. WATTS AND S. H. STROGATZ, Collective dynamics of "small-world" networks, Nature, 393 (1998), pp. 440-442.
25. D. J. WATTS, Small Worlds: The Dynamics of Networks between Order and Randomness, Princeton University Press, Princeton, NJ, 1999.
26. H. JEONG, B. TOMBOR, R. ALBERT, Z. N. OLTVAI, AND A.-L. BARABASI, The large-scale organization of metabolic networks, Nature, 407 (2000), pp. 651-654.
27. S. H. STROGATZ, Exploring complex networks, Nature, 268 (2001), pp. 268-276.
28. Y. KURAMOTO, Chemical Oscillations, Waves, and Turbulence, Springer-Verlag, New York, 1984.
29. T. BOHR AND O. B. CHRISTENSEN, Size dependence, coherence, and scaling in turbulent coupled-map lattices, Phys. Rev. Lett., 63 (1989), pp. 2161-2164.
30. L. A. BUNIMOVICH, A. LAMBERT, AND R. LIMA, The emergence of coherent structures in coupled map lattices, J. Statist. Phys., 61 (1990), pp. 253-262.
31. O. CARDOSO, H. WILLAIME, AND P. TABELING, Short-wavelength instability in a linear array of vortices, Phys. Rev. Lett., 65 (1990), pp. 1869-1872.
32. J. F. HEAGY, L. M. PECORA, AND T. L. CARROLL, Short wavelength bifurcations and size instabilities in coupled oscillator systems, Phys. Rev. Lett., 74 (1995), pp. 4185-4188.
33. C. JUANG, T. M. HUANG, J. JUANG, AND W. W. LIN, A synchronization scheme using self-pulsating laser diodes in optical communication, IEEE J. Quantum Electron., 36 (2000), pp. 300-304.
34. G. RANGARAJAN AND M. DING, Stability of synchronized chaos in coupled dynamical systems, Phys. Lett. A, 296 (2002), pp. 204-209.