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Principles of Discontinuous Dynamical Systems pp 55–80Cite as

Nonautonomous Systems with Variable Moments of Impulses

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Abstract

Let \(G \subset {\mathbb{R}}^{n}\) be an open and connected set, I an open interval in \(\mathbb{R},\) and \(\mathcal{A}\) an interval in \(\mathbb{Z}.\) We consider the following system:

$$\begin{array}{rcl} & & x^\prime = f(t,x), \\ & & \Delta x{\vert }_{t={\tau }_{i}(x)} ={J}_{i}(x),\end{array}$$
(5.1)

where \((t,i,x) \in I \times \mathcal{A}\times G,\) the function f(t, x) is continuous on I ×G, functions J i are defined on G, and \({\tau }_{i}(x),i \in \mathcal{A},\) are continuous on G functions.

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  1. Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey

    Marat Akhmet

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Akhmet, M. (2010). Nonautonomous Systems with Variable Moments of Impulses. In: Principles of Discontinuous Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6581-3_5

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