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

Abstract We analyze some global, generic properties of a pair of coupled maps. These generic properties are then utilized to investigate how the extent of coupling affects the behavior of the coupled system. Quasi-symmtery of the global behavior is discussed. Numerical validation of the analytical results is provided.

[1]  F. Udwadia,et al.  Dynamics of coupled nonlinear maps and its application to ecological modeling , 1997 .

[2]  Tomasz Nowicki,et al.  Some phase transitions in coupled map lattices , 1992 .

[3]  Cuomo,et al.  Circuit implementation of synchronized chaos with applications to communications. , 1993, Physical review letters.

[4]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[5]  W. Singer,et al.  Oscillatory Neuronal Responses in the Visual Cortex of the Awake Macaque Monkey , 1992, The European journal of neuroscience.

[6]  P. Grassberger,et al.  Symmetry breaking bifurcation for coupled chaotic attractors , 1991 .

[7]  Hidetsugu Sakaguchi,et al.  Bifurcations of the Coupled Logistic Map , 1987 .

[8]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .

[9]  G. Benettin,et al.  Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application , 1980 .

[10]  Firdaus E. Udwadia,et al.  An efficient QR based method for the computation of Lyapunov exponents , 1997 .

[11]  Martin,et al.  New method for determining the largest Liapunov exponent of simple nonlinear systems. , 1986, Physical review. A, General physics.

[12]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. II: The Mapping Approach , 1983 .

[13]  W. Ricker.  Stock and Recruitment , 1954 .

[14]  M. Gyllenberg,et al.  Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model. , 1993, Mathematical biosciences.

[15]  Bifurcation in a coupled logistic map. Some analytic and numerical results , 1991 .

[16]  Alan V. Oppenheim,et al.  Circuit implementation of synchronized chaos with applications to communications. , 1993, Physical review letters.

[17]  W. Singer,et al.  Temporal coding in the visual cortex: new vistas on integration in the nervous system , 1992, Trends in Neurosciences.