Dynamics, stability, and statistics on lattices and networks (Q2879377)

The work presents a very comprehensive review of the wide aspects of dynamical and stochastic behaviour of coupled systems. The explanation is consequent and allows the reader to study the considered questions starting from the very basics, e.g., principal topologies of lattices and networks, methods of stability analysis, chaos detection, etc. The principal objects are coupled dynamical systems, which are also considered in connection with the discretization of partial differential equations describing diffusion and heat conduction. The principal examples are homogeneous and disordered harmonic chains and the interplay dynamical solutions with the stochastic Fokker-Planck approach as well as the Boltzmann-Peierls approach to anharmonic disordered systems, generated temperature distributions, heat and energy fluxes, issues addressed to mode interactions, distribution of perturbations, localization. A special attention is drawn to modern topics of anomalous transport in regular systems and disordered networks. The text is sullied with a comprehensive bibliography and can serve as a high-quality tutorial or reference source.