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Stability and Bifurcation Theory for Non-Autonomous Differential Equations pp 185–263Cite as

Non-autonomous Functional Differential Equations and Applications

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Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2065))

Abstract

This chapter deals with the applications of dynamical systems techniques to the study of non-autonomous, monotone and recurrent functional differential equations. After introducing the basic concepts in the theory of skew-product semiflows and the appropriate topological dynamics techniques, we study the long-term behavior of relatively compact trajectories by describing the structure of minimal and omega-limit sets, as well as the attractors. Both the cases of finite and infinite delay are considered. In particular, we show the relevance of uniform stability in this study. Special attention is also paid to the almost periodic case, in which the presence of almost periodic and almost automorphic dynamics is analyzed. Some applications of these techniques to the study of neural networks, compartmental systems and certain biochemical control circuit models are shown.

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Acknowledgements

The authors were partly supported by Junta de Castilla y León under project VA060A09, and Ministerio de Ciencia e Innovación under project MTM2008-00700/MTM.

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    Sylvia Novo & Rafael Obaya

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Novo, S., Obaya, R. (2013). Non-autonomous Functional Differential Equations and Applications. In: Stability and Bifurcation Theory for Non-Autonomous Differential Equations. Lecture Notes in Mathematics(), vol 2065. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32906-7_4

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