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A Few Other Interesting Chaotic Delay Differential Equations

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Dynamics of Nonlinear Time-Delay Systems

Part of the book series: Springer Series in Synergetics ((SSSYN))

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Abstract

One of the well known properties of DDEs is that their effective dimensions increase with the delay time τ[1, 2], see Sect. 1.2.2. This allows one to select different values (sufficiently large) for the delay time τ to generate high-dimensional chaotic signals. Hence, in recent times DDEs have received increased attention in the nonlinear dynamics literature due to the possibility of generating more complex and high-dimensional chaotic attractors and also because of the feasibility of their experimental realization. Therefore, several chaotic time-delay systems and their variants have been proposed during the past few years for generating and enhancing complexity of chaotic behavior in various technological and engineering applications. In this chapter, we will briefly review the dynamical properties of some of the most important first order scalar nonlinear time-delay systems, that have been widely used in the literature, exhibiting chaotic/hyperchaotic behaviors. In addition, we will also present some of the interesting coupled (higher order) delay differential equations in different areas of science and technology.

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Authors and Affiliations

  1. Centre for Nonlinear Dynamics, Bharathidasan University, Palkalaiperur Campus, Tiruchirapalli, 620 024, India

    Prof. Dr. M. Lakshmanan

  2. Transdisciplinary Concepts and Methods, Potsdam Institute for Climate Impact Research, Telegrafenberg, 14412, Potsdam, Germany

    Dr. D.V. Senthilkumar

Authors
  1. Prof. Dr. M. Lakshmanan
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  2. Dr. D.V. Senthilkumar
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Correspondence to M. Lakshmanan .

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Lakshmanan, M., Senthilkumar, D. (2011). A Few Other Interesting Chaotic Delay Differential Equations. In: Dynamics of Nonlinear Time-Delay Systems. Springer Series in Synergetics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14938-2_4

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  • DOI: https://doi.org/10.1007/978-3-642-14938-2_4

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