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

2000  
We show how certain Ndimensional dynamical systems are able to exploit the full instability capabilities of their fixed points to do Hopf bifurcations and how such a behavior produces complex time evolutions based on the nonlinear combination of the oscillation modes that emerged from these bifurcations. For really different oscillation frequencies, the evolutions describe robust wave form structures, usually periodic, in which selfsimilarity with respect to both the time scale and system dimension is clearly appreciated. For closer frequencies, the evolution signals usually appear irregular but are still based on the repetition of complex wave form structures. The study is developed by considering vector fields with a scalarvalued nonlinear function of a single variable that is a linear combination of the N dynamical variables. In this case, the linear stability analysis can be used to design Ndimensional systems in which the fixed points of a saddlenode pair experience up to N21 Hopf bifurcations with preselected oscillation frequencies. The secondary processes occurring in the phase region where the variety of limit cycles appear may be rather complex and difficult to characterize, but they produce the nonlinear mixing of oscillation modes with relatively generic features  
application/pdf  
003732  
15393755 (versiÃ³ paper) 15502376 (versiÃ³ electrÃ²nica) 

http://hdl.handle.net/10256/7699  
eng  
American Physical Society  
ReproducciÃ³ digital del document publicat a: http://link.aps.org/doi/10.1103/PhysRevE.62.333 Articles publicats (DF) 

Â© Physical Review E, 2000, vol. 62, nÃºm. 1, p. 333348  
Tots els drets reservats  
Sistemes dinÃ mics diferenciables
Differentiable dynamical systems Hespais Hspaces OscilÂ·lacions no lineals Nonlinear oscillations 

Full instability behavior of Ndimensional dynamical systems with a onedirectional nonlinear vector field  
info:eurepo/semantics/article  
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