Work

Analytical results for coupled-map lattices with long-range interactions

Year: 2003

Type: article

Abstract: We obtain exact analytical results for lattices of maps with couplings that decay with distance as r(-alpha). We analyze the effect of the coupling range on the system dynamics through the Lyapunov spectrum. For lattices whose elements are piecewise linear maps, we get an algebraic expression for the Lyapunov spectrum. When the local dynamics is given by a nonlinear map, the Lyapunov spectrum for a completely synchronized state is analytically obtained. The critical line characterizing the synchronization transition is determined from the expression for the largest transversal Lyapunov exponent. In particular, it is shown that in the thermodynamical limit, such transition is only possible for sufficiently long-range interactions, namely, for alpha

Source: Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

DOI: 10.1103/physreve.68.045202

Authors: Celia Anteneodo, Sandro E. de S. Pinto, Antônio M. Batista, Ricardo L. Viana

Institutions: Centro Brasileiro de Pesquisas Físicas, Universidade Federal do Paraná, Universidade Estadual de Ponta Grossa

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2069218356

FWCI: 6.977

Cites: 45

Cited by: 57

Related to: 10