Ítem
Rius, J.
Figueras, M. Herrero, R. Farjas Silva, Jordi Pi i Vila, Francesc Orriols Tubella, Gaspar 

2000  
We report experimental and numerical results showing how certain Ndimensional dynamical systems are able to exhibit complex time evolutions based on the nonlinear combination of N1 oscillation modes. The experiments have been done with a family of thermooptical systems of effective dynamical dimension varying from 1 to 6. The corresponding mathematical model is an Ndimensional vector field based on a scalarvalued 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 saddlenode 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 wellorganized 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  
application/pdf  
10541500 (versió paper) 10897682 (versió electrònica) 

http://hdl.handle.net/10256/7834  
eng  
American Institute of Physics  
Reproducció digital del document publicat a: http://dx.doi.org/10.1063/1.1324650 Articles publicats (DF) 

© Chaos, 2000, vol. 10, núm. 4, p. 760770  
Tots els drets reservats  
Sistemes dinàmics diferenciables
Differentiable dynamical systems Hespais Hspaces Oscil·lacions no lineals Nonlinear oscillations 

Ndimensional dynamical systems exploiting instabilities in full  
info:eurepo/semantics/article  
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