Nonlinearly driven transverse synchronization in coupled chaotic systems
Anno: 2005
Autori: Cencini M., Torcini A.
Affiliazione autori: ISC-CNR, Via dei Taurini 19, 00185 Roma, Italy;
SMC-INFM, Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale A. Moro 2, 00185 Roma,I taly;
ISC-CNR and Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy
INFM, SMC; Ist Nazl Ott Applicata.
Abstract: Synchronization transitions are investigated in coupled chaotic maps. Depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur. When only two maps are considered we always find that the critical coupling epsilon(1) for chaotic synchronization can be predicted within a linear analysis by the vanishing of the transverse Lyapunov exponent lambda(T). However, major differences between transitions driven by linear or nonlinear mechanisms are revealed by the dynamics of the transient toward the synchronized state. As a representative example of extended systems a one dimensional lattice of chaotic maps with power-law coupling is considered. In this high dimensional model finite amplitude instabilities may have a dramatic effect on the transition. For strong nonlinearities an exponential divergence of the synchronization times with the chain length can be observed above epsilon(1), notwithstanding the transverse dynamics is stable against infinitesimal perturbations at any instant. Therefore, the transition takes place at a coupling epsilon(nl) definitely larger than epsilon(1) and its origin is intrinsically nonlinear. The linearly driven transitions are continuous and can be described in terms of mean field results for non-equilibrium phase transitions with long range interactions. While the transitions dominated by nonlinear mechanisms appear to be discontinuous. (c) 2005 Elsevier B.V. All rights reserved.
Giornale/Rivista: PHYSICA D-NONLINEAR PHENOMENA
Volume: 208 (3-4) Da Pagina: 191 A: 208
Maggiori informazioni: We are grateful to W. Just, A. Politi and A. Pikovsky for useful discussions and remarks and to F. Ginelli also for a careful reading of this manuscript. Partial support from the Italian FIRB contract no. RBNE01CW3M_001 is acknowledged. Parole chiavi: synchronization; coupled chaotic systems; linear and nonlinear instabilities; coupled map latticesDOI: 10.1016/j.physd.2005.06.017Citazioni: 10dati da “WEB OF SCIENCE” (of Thomson Reuters) aggiornati al: 2025-05-18Riferimenti tratti da Isi Web of Knowledge: (solo abbonati) Link per visualizzare la scheda su IsiWeb: Clicca quiLink per visualizzare la citazioni su IsiWeb: Clicca qui
