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Stability and Hopf Bifurcation for a First-Order Delay Differential Equation with Distributed Delay

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Complex Time-Delay Systems

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

This class of equations is widely used in many research fields—it can be obtained through the linearization of different nonlinear problems (see, for example, Sect. 8.5)—such as automatic, economic, and, for our purpose, in biological modeling because it can be associated with problems in which it is important to take into account some history of the state variable (e.g., gestation period, cell cycle durations, or incubation time [23, 35]).

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Authors and Affiliations

  1. Université de Lyon; Université Lyon 1, CNRS UMR5208 Institut Camille Jordan, 43 blvd du 11 novembre 1918, F-69622, Villeurbanne-Cedex, France

    Fabien Crauste

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  1. Fabien Crauste
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Correspondence to Fabien Crauste .

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  1. Wissenschaften, MPI für Mathematik in den, Inselstr. 22-26, Leipzig, 04103, Germany

    Fatihcan M. Atay

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Crauste, F. (2009). Stability and Hopf Bifurcation for a First-Order Delay Differential Equation with Distributed Delay. In: Atay, F. (eds) Complex Time-Delay Systems. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02329-3_8

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  • DOI: https://doi.org/10.1007/978-3-642-02329-3_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02328-6

  • Online ISBN: 978-3-642-02329-3

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