Chaos and Regularity in Adaptive Lattice Dynamics

Abstract

We describe the rich spectrum of spatio-temporal phenomena emerging from a class of models incorporating adaptive dynamics on a lattice of nonlinear (typically chaotic) elements. The investigation is based on extensive numerical simulations which reveal many novel dynamical patterns, including scaling properties (as exemplified, for instance, by distinct 1/f spectral characteristics) emerging from processes operating over a range of time and length scales. Moreover, we study the simpler case of unidirectional adaptive dynamics rigorously, and this provides an analytical understanding of the dynamical reasons underlying the many phases found in these models.