Ítem


N-dimensional dynamical systems exploiting instabilities in full

We report experimental and numerical results showing how certain N-dimensional dynamical systems are able to exhibit complex time evolutions based on the nonlinear combination of N-1 oscillation modes. The experiments have been done with a family of thermo-optical systems of effective dynamical dimension varying from 1 to 6. The corresponding mathematical model is an N-dimensional vector field based on a scalar-valued nonlinear function of a single variable that is a linear combination of all the dynamic variables. We show how the complex evolutions appear associated with the occurrence of successive Hopf bifurcations in a saddle-node pair of fixed points up to exhaust their instability capabilities in N dimensions. For this reason the observed phenomenon is denoted as the full instability behavior of the dynamical system. The process through which the attractor responsible for the observed time evolution is formed may be rather complex and difficult to characterize. Nevertheless, the well-organized structure of the time signals suggests some generic mechanism of nonlinear mode mixing that we associate with the cluster of invariant sets emerging from the pair of fixed points and with the influence of the neighboring saddle sets on the flow nearby the attractor. The generation of invariant tori is likely during the full instability development and the global process may be considered as a generalized Landau scenario for the emergence of irregular and complex behavior through the nonlinear superposition of oscillatory motions

© Chaos, 2000, vol. 10, núm. 4, p. 760-770

American Institute of Physics

Autor: Rius, J.
Figueras, M.
Herrero, R.
Farjas Silva, Jordi
Pi i Vila, Francesc
Orriols Tubella, Gaspar
Data: 2000
Resum: We report experimental and numerical results showing how certain N-dimensional dynamical systems are able to exhibit complex time evolutions based on the nonlinear combination of N-1 oscillation modes. The experiments have been done with a family of thermo-optical systems of effective dynamical dimension varying from 1 to 6. The corresponding mathematical model is an N-dimensional vector field based on a scalar-valued nonlinear function of a single variable that is a linear combination of all the dynamic variables. We show how the complex evolutions appear associated with the occurrence of successive Hopf bifurcations in a saddle-node pair of fixed points up to exhaust their instability capabilities in N dimensions. For this reason the observed phenomenon is denoted as the full instability behavior of the dynamical system. The process through which the attractor responsible for the observed time evolution is formed may be rather complex and difficult to characterize. Nevertheless, the well-organized structure of the time signals suggests some generic mechanism of nonlinear mode mixing that we associate with the cluster of invariant sets emerging from the pair of fixed points and with the influence of the neighboring saddle sets on the flow nearby the attractor. The generation of invariant tori is likely during the full instability development and the global process may be considered as a generalized Landau scenario for the emergence of irregular and complex behavior through the nonlinear superposition of oscillatory motions
Format: application/pdf
ISSN: 1054-1500 (versió paper)
1089-7682 (versió electrònica)
Accés al document: http://hdl.handle.net/10256/7834
Llenguatge: eng
Editor: American Institute of Physics
Col·lecció: Reproducció digital del document publicat a: http://dx.doi.org/10.1063/1.1324650
Articles publicats (D-F)
És part de: © Chaos, 2000, vol. 10, núm. 4, p. 760-770
Drets: Tots els drets reservats
Matèria: Sistemes dinàmics diferenciables
Differentiable dynamical systems
H-espais
H-spaces
Oscil·lacions no lineals
Nonlinear oscillations
Títol: N-dimensional dynamical systems exploiting instabilities in full
Tipus: info:eu-repo/semantics/article
Repositori: DUGiDocs

Matèries

Autors