Abstract:
The article is devoted to the development of Lyapunov methods for analyzing the instability of the equilibrium of a dynamical system in the space of probability measures, given by the nonlocal continuity equation. We consider the case of non-smooth Lyapunov function, but barycentrically subdifferentiable only. Sufficient instability conditions are obtained, which are an analogue of the Chetaev theorem and are based on an analysis of the behavior of the non-smooth Lyapunov function in the neighbourhood of the equilibrium. Also we give an example of a dynamical system, the instability of whose equilibrium position is proved using the obtained theorem.
Keywords:non-local continuity equation, Lyapunov second method, non-smooth Lyapunov function, instability, derivatives in the space of measures
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