ar X iv : n lin / 0 30 20 14 v 1 [ nl in . C D ] 6 F eb 2 00 3 Fluctuational transitions through a fractal basin boundary

Fluctuational transitions across locally-disconnected and locally-connected fractal basin boundaries

We study fluctuational transitions in a discrete dynamical system that has two co-existing attractors in phase space, separated by a fractal basin boundary which may be either locally-disconnected or locally-connected. It is shown that, in each case, transitions occur via an accessible point on the boundary. The complicated structure of paths inside the locally-disconnected fractal boundary is ...

ar X iv : c on d - m at / 0 50 20 77 v 1 2 F eb 2 00 5 HIGHER MOMENTS OF NOISE

ar X iv : n lin / 0 51 10 57 v 1 [ nl in . C D ] 2 6 N ov 2 00 5 DISCRETE DYNAMICAL SYSTEMS EMBEDDED IN CANTOR SETS

While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with N variables, as binary neural networks and cellular automata. The main difficulty is the choice of a suitable topology to study the limit N → ∞. By embedding the discrete phase space into a Cantor set we provided a natural setting to define topological e...

ar X iv : 0 90 2 . 10 22 v 1 [ nl in . S I ] 6 F eb 2 00 9 Wakimoto realization of the elliptic algebra U q , p ( ŝl N )

We construct a free field realization of the elliptic quantum algebra Uq,p(ŝlN ) for arbitrary level k 6= 0,−N . We study Drinfeld current and the screening current associated with Uq,p(ŝlN ) for arbitrary level k. In the limit p → 0 this realization becomes q-Wakimoto realization for Uq(ŝlN ).

Fluctuational transitions across different kinds of fractal basin boundaries.

We study fluctuational transitions in discrete and continuous dynamical systems that have two coexisting attractors in phase space, separated by a fractal basin boundary which may be either locally disconnected or locally connected. Theoretical and numerical evidence is given to show that, in each case, the transition occurs via a unique accessible point on the boundary, both in discrete system...