The spatially-temporal chaos and the theory of infinite-dimensional systems of ordinary differential equations originating in some physical problems

In the paper an infinite-dimensional systems of ordinary differential equations is studied, which have applications to some popular and important physical problems. The theory of such systems is constructed. This theory includes the description of all stationary solutions, constructions of phase spaces and the proof of unique solvability of solutions, the formulation and the proof of a criterion of asymptotic stability and the construction of strange attractors. The proofs of main results are based on the geometry of many-dimensional lattice. The principal result is the appearance of spatially temporal chaos in the infinite-dimensional space of such systems which explaines some physical phenomenons.