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Bubbling transition to spatial mode excitation in an extended dynamical system
Authors:J.D. Szezech Jr.  R.L. Viana  I.L. Caldas
Affiliation:a Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531-990, Curitiba, Paraná, Brazil
b Instituto de Física, Universidade de São Paulo, 05315-970, São Paulo, São Paulo, Brazil
Abstract:We investigated the transition to spatio-temporal chaos in spatially extended nonlinear dynamical systems possessing an invariant subspace with a low-dimensional attractor. When the latter is chaotic and the subspace is transversely stable we have a spatially homogeneous state only. The onset of spatio-temporal chaos, i.e. the excitation of spatially inhomogeneous modes, occur through the loss of transversal stability of some unstable periodic orbit embedded in the chaotic attractor lying in the invariant subspace. This is a bubbling transition, since there is a switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency. Hence the onset of spatio-temporal chaos depends critically both on the existence of a chaotic attractor in the invariant subspace and its being transversely stable or unstable.
Keywords:Spatio-temporal chaos   Transition to turbulence   Spatial mode excitation   Three-wave interaction
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