On the roughness of nonlinear dynamic systems

The conditions under which the stability type of the equilibrium state of a Lyapunov-type random-order nonlinear dynamic system would not change under any relatively small linear or nonlinear perturbances of its right-hand member (roughness in the sense of stability type conservation). Nonlinear components of right-hand members of the original (unperturbed) system and nonlinear perturbances of those right-hand members are considered to belong to a wide class of nonlinear functions containing both analytic functions and various classes of nonanalytic functions. Sufficient and necessary roughness conditions are derived.