The role of nonlinearities in the dynamics of the non-equilibrium systems is considered. Various types of nonlinearities for dynamical systems with holonomic and nonholonomic constraints are studied. Features of the nonlinearity responsible for the evolution of the systems to the equilibrium are considered. The interrelation of the nonlinearities with the concepts of symmetry breaking is analyzed. Mathematical justification of the irreversibility of the dynamics of systems is offered. Peculiarities of nonlinear nonequilibrium systems connected with hierarchical structure of natural objects are studied.
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