Generation of quasiperiodic oscillations in pairs of coupled maps - Rech P.C.* (2007)
We investigate analytically the emergence of quasiperiodic and mode-locked states of arbitrary period in pairs of coupled maps. Quasiperiodic and mode-locked states arise from Naimark-Sacker bifurcations and exhibit very rich local dynamics. We determine analytically both states for pairs of maps under symmetric and asymmetric couplings. Lyapunov spectra, portraits in parameter-space and in phase-space are used to show the transition from quasiperiodic and from mode-locked states into chaotic states and to check the range of validity of the approximations implicit in the standard normal forms. © 2006 Elsevier Ltd. All rights reserved.