Localised modes on localised equilibria

Abstract

We show that spatially localised equilibrium for networks of dynamical systems can have localised eigenmodes on them, and study their spectral properties and onset thresholds. The theory is illustrated with numerics for a class of one-dimensional one-degree-of-freedom Hamiltonian oscillator chains with nearest neighbour coupling, which have a discrete kink in the uncoupled limit, We discuss implications of localised eigenmodes on spatially localised equilibria on many aspects of localised dynamics of networks, Copyright (C) 1998 Elsevier Science B.V.