Recently, the concept of measure differential equation was introduced by Piccoli. Such a concept allows deterministic modeling of uncertainty, finite-speed diffusion, concentration, and other phenomena. Moreover, it represents a natural generalization of Ordinary Differential Equations to measures.\\ In this paper, we deal with the stability of fixed points for measure differential equations. In particular, we discuss two concepts related to classical Lyapunov stability in terms of measure support and first moment. The two concepts are not comparable, but the latter implies the former if the measure differential equation is defined by an ordinary one. Finally, we provide results concerning Lyapunov functions.
Lyapunov stability for measure differential equations
C. D'Apice;R. Manzo;B. Piccoli
;V. Vespri
2024-01-01
Abstract
Recently, the concept of measure differential equation was introduced by Piccoli. Such a concept allows deterministic modeling of uncertainty, finite-speed diffusion, concentration, and other phenomena. Moreover, it represents a natural generalization of Ordinary Differential Equations to measures.\\ In this paper, we deal with the stability of fixed points for measure differential equations. In particular, we discuss two concepts related to classical Lyapunov stability in terms of measure support and first moment. The two concepts are not comparable, but the latter implies the former if the measure differential equation is defined by an ordinary one. Finally, we provide results concerning Lyapunov functions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
