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Nonautonomous Systems with Variable Moments of Impulses

In: Principles of Discontinuous Dynamical Systems

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  • Marat Akhmet

    (Middle East Technical University, Department of Mathematics)

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

Suggested Citation

  • Marat Akhmet, 2010. "Nonautonomous Systems with Variable Moments of Impulses," Springer Books, in: Principles of Discontinuous Dynamical Systems, chapter 0, pages 55-80, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-6581-3_5
    DOI: 10.1007/978-1-4419-6581-3_5
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