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Differentiability Properties of Nonautonomous Systems

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Principles of Discontinuous Dynamical Systems

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Abstract

In this chapter, we investigate the fundamental properties of differential equations with variable moments of impulses: differential and analytic dependence of solutions on initial conditions and parameters. Differentiability of solutions is the property, which is of underestimated importance for differential equations. One needs the conditions, which provide the smoothness of solutions if a system is to be linearized around a certain solution, to prove the existence of periodic and almost periodic solutions in critical and noncritical cases by using the method of small parameter [105, 107], to investigate problems of synchronization and bifurcation theory.

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Authors and Affiliations

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

    Marat Akhmet

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  1. Marat Akhmet
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Correspondence to Marat Akhmet .

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Akhmet, M. (2010). Differentiability Properties of Nonautonomous Systems. In: Principles of Discontinuous Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6581-3_6

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