  This thesis focuses on the mechanisms of energy transport in multidimensional
heterogeneous lattice models, studying in particular the case of the
Klein-Gordon model of coupled anharmonic oscillators in one and two spatial
dimensions. We report the effects of the type of the impurity (heterogeneity)
parameter on the systems' transport properties and classifies the transport
mechanisms of the nonlinear versions of the models into various dynamical
regimes. We also identify computationally efficient numerical integration
techniques, including the so-called symplectic integrators, and implement them
for studying these models. Finally, we perform an extensive numerical
investigation of the dynamics of the considered models revealing that for their
nonlinear versions chaotic transport persists and chaotic hotspots meander in
the region of energy concentration supporting the spreading mechanism.
