Exponential stability of equilibria of differential equations with time-dependent delay and non-Lipschitz nonlinearity ☆

Abstract This paper studies stability of equilibria of differential equations with time-dependent delay and non-Lipschitz nonlinearity. For this class of problems, we develop a novel method of analysis, the relative nonlinear measure method. Using this method, we obtain a sufficient condition for exponential stability. Moreover, this condition is used to study the stability of the equilibrium of a neural network model. Finally, some examples illustrate that our results are improvement and extension of some existing ones.

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