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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
