Some global properties of a pair of coupled maps: Quasi-symmetry, periodicity, and synchronicity

Physica D: Nonlinear Phenomena

Volumn 111, Issue 1-4, 1998, Pages 16-26

  Udwadia, F E ^a   Raju, N ^a,b  

^a University of Southern California ^*  (United States)

^b UMEVoice   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010607196     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)80002-4     Document Type: Article

References (18)

1. G. Bennetin, L. Galgani and J.M. Strelcyn, The Lyapunov characteristic exponents for a smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 2: Numerical application. Meccanica 15 (1980) 21.
2. R.A. Chowdhury and K. Chowdhury, Bifurcations in a coupled logistic map, Int. J. Theor. Phys. 30 (1991) 97.
3. K.M. Cuomo and A.V. Oppenheim, Circuit implementation of synchronized chaos with application to communications, Phys. Rev. Lett. 71 (1993) 65.
4. A. Engel, P. Konig, A. Kreiter, T. Schillen and W. Singer, Temporal coding in the visual cortex: New vistas on integration in the nervous system, Trends Neurosci. 15 (1992) 218.
5. H. Fujisaka and T. Yamada, Stability theory of synchronized motion in coupled-oscillator systems, Progr. Theor. Phys. 69 (1983) 32.
6. M. Gyllenberg, G. Soderbacka and S. Ericsson, Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model, Math. Biosci. 118 (1992) 25.
7. G. Keller, M. Kunzle and T. Nowicki, Some phase transitions in coupled map lattices. Physica D 59 (1992) 39.
8. A.K. Kreiter and W. Singer, Oscillatory neuronal responses in the visual cortex of the awake monkey, Eur. J. Neurosci. 4 (1992) 369.
9. M.S. Livingston, Visually-evoked oscillations in money striate cortex, Soc. Neurosci. Abstr. 17 (1991) 73.3.
10. R.M. May, Simple mathematical models with very complicated dynamics, Nature 261 (1976) 459.
11. L. Pecora and T. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64 (1990) 821.
12. P. Pikovsky and A.S. Grassberger, Symmetry breaking bifurcation for coupled attractors. J. Phys. A 24 (1991) 4587.
13. W.E. Ricker, Stock and recruitment, J. Fish. Res. Board. Canada 11 (1954) 559.
14. H.G. Schuster, S. Martin and W. Martienssen, New method for determining the largest Lyapunov exponent of simple nonlinear systems, Phys. Rev. A 33 (1986) 3347.
15. F.E. Udwadia and R.S. Guttalu, Chaotic dynamics of a piecewise cubic map, Phys. Rev. A 40 (1989) 4032.
16. F.E. Udwadia and N. Raju, Dynamics of coupled nonlinear maps and its application to ecological modeling, Appl. Math. Comput. 82 (1997) 137.
17. H. von Bremen, F.E. Udwadia and W. Proskurowski, An efficient qr based method for the computation of Lyapunov exponents, Physica D 101 (1997) 1.
18. T. Yamada and H. Fujisaka, Stability theory of synchronized motion in coupled-oscillator systems. II - the mapping approach, Progr. Theor. Phys. 70 (1983) 1240.