Periodic, quasiperiodic, and chaotic localized solutions of a driven, damped nonlinear lattice

We study the solution behavior of a damped and parametrically driven nonlin ear chain modeled by a discrete nonlinear Schrodinger equation. Special att ention is paid to the impact of the damping and driving terms on the existe nce and stability of localized solutions. Dependent upon the strength of th e driving force, we find rich lattice dynamics such as stationary solitonli ke solutions and periodic and quasiperiodic breathers, respectively. The la tter are characterized by regular motion on tori in phase space. For a crit ical driving amplitude the torus is destroyed in the course of time, leavin g temporarily a chaotic breather on the lattice. We call this order-chaos t ransition a dynamical quasiperiodic route to chaos. Eventually the chaotic breather collapses to a stable localized multisite state. Finally, it is de monstrated that above a certain amplitude of the parametric driving force n o localized states exist. [S1063-651X(99)04202-6].