Universality in active chaos

Universality in active chaos.

Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such processes, hydrodynamical stirring strongly couples into the reactivity of the advected species and might thus make the traditional treatment of the problem thr...

Universality, Tolerance, Chaos and Order

What is the minimum possible number of edges in a graph that contains a copy of every graph on n vertices with maximum degree a most k ? This question, as well as several related variants, received a considerable amount of attention during the last decade. In this short survey we describe the known results focusing on the main ideas in the proofs, discuss the remaining open problems, and mentio...

Universality in Chaos: Evolution of Turbulence

Universality In Chaos - The Logistic Map

In this seminar, we are going to look at the period-doubling approach to chaos. It is indeed a remarkable fact that all systems which make a transition from order to disorder by the period-doubling route, irrespective of the exact functional forms that represent these systems, display common properties. It turns out that given certain qualitative constraints on the system considered, thus allow...

Routes to chaos, universality and glass formation

We review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period doubling, intermittency, and quasiperiodicity routes. In these situations the dynamical behavior is exactly describable through infinite families of Tsallis’ q-expon...