In the paper, we consider a linear nonautonomous Goursat-Darboux system which is a continuous version of discrete Fornasini-Marchesini system. We give some general algorithm for construction a piecewise constant control related to some density result for attainable sets connected with integrable controls and piecewise constant ones. Copyright c ©2005 IFAC

We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our of very general form provided that the perturbations well-behaved, we do not assume any asymptotic behaviour system. Moreover, control on may differ along finitely many mutually complementary directions. consider both cases one-sided discrete continuo...

Stable fiber bundles are the nonautonomous analog of stable manifolds and these objects provide valuable information on the underlying dynamics. We propose an algorithm for their computation that applies to a wide class of models, including noninvertible and nonautonomous discrete time systems. Precise error estimates are provided and fiber bundles are computed for several examples.

We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DA...

We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous, i.e. coupling constants, particle masses and on-site potentials can have small variations along the chain. We look for small amplitude and time-periodic solutions, and in particular spatially localized ones (discrete bre...