STABILITY PRESERVATION OF EQUILIBRIUM STATES FOR A CLASS OF SYSTEMS OF NONLINEAR DIFFERENTIAL-EQUATIONS

A problem for stability preservation of the equilibrium states of nonlinear systems during finite variations of their parameters is stated. Sufficient stability conditions of the equilibrium states for multidimensional systems of nonlinear differential equations with special structures are defined. In the space of parameters of these systems, stability-preservation regions for the equilibrium states are found under changes of the parameters which determine the processes in original nonlinear systems. Use is made of the boundedness of a phase space and the informative meaning of the parameters and characteristics of the processes under examination.