On reduction instability conditions for nonlinear dynamical systems

Abstract New instability conditions for some classes of nonlinear dynamical systems of an arbitrary order are considered. These conditions reduce the investigation of instability of the initial nonlinear system to the investigation of instability of the linearized system. In this connection, the con...
Ausführliche Beschreibung

Abstract New instability conditions for some classes of nonlinear dynamical systems of an arbitrary order are considered. These conditions reduce the investigation of instability of the initial nonlinear system to the investigation of instability of the linearized system. In this connection, the considered conditions are similar to the hypothesis of the instability theorem of the first Lyapunov method (the stability investigation by the first approximation), but they are applicable to more complicated nonlinear systems, because it takes into account the non-autonomy of the linearized system and the fact that the nonlinear terms in the right-hand sides of the equations of the initial system belong not only to the class of analytical functions. For different classes of the nonlinear systems, sufficient instability conditions are presented. Ausführliche Beschreibung