Investigation of Chaos Arising Conditions in the Distributed Systems

In this report the results of investigation if dynamics chaos arising in distributed system conditioned by cubic and quadratic nonlinearities are presented. It was pointed that when there is quadratic nonlinearity the chaos arises at smaller amplitudes than at cubic nonlinearity. I.e. quadratic nonlinearity is more important for arising of dynamic chaos. The chaotic character of the investigated dynamic is proved by calculation of spectrum, correlation function and high Lyapunov exponent. The algorithm of characteristic numbers investigation of the differential equations set was proposed. This allows to define the region of the local instability in the phase space and, accordingly, to formulate chaos arising criterion for the wide class of dynamic systems.