Abstract
The instability of nonlinear nonautonomous dynamic systems of arbitrary order is studied. A special class of parameter-dependent scalar functions is used in Part I, which describes the preliminaries, to derive new necessary and sufficient conditions for the instability of equilibrium states of such systems. In Part II, these special functions are used to express new sufficient conditions of instability for a particular class of unstable nonlinear dynamic systems in terms of functions having a simple geometric meaning.
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