This paper discusses coupled map networks of arbitrary sizes over arbitrary graphs; the local dynamics are taken to be diffeomorphisms or expanding maps of circles. A connection is made to hyperbolic theory: increasing coupling strengths leads to a cascade of bifurcations in which unstable subspaces in the coupled map systematically become stable. Concrete examples with different network architectures are discussed.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics