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Nonlinear delay differential equations with a slow integral term: fundamental issues & applications in photonics

Held by Prof. Laurent Larger (University of Franche-Comte, Besancon, France)
28.04.2016, 12:00 Uhr


Delay equations are described in the literature with famous paradigmatic models, e.g. from life science (Mackey-Glass model for blood cell production dynamics), or from optics (Ikeda ring cavity model). Beyond these famous equations illustrating many particular features of delay equations (period doubling route to chaos, high dimensional chaos), applications dedicated to optical chaos communications led to the derivation of a variations of these model, sometimes referred to as integro-differential delay equations instead of delay differential equations. The additional slow integral term involved in this specific subclass of delay dynamics has then triggered the discovery of sevral fundamental properties that are not exhibited by the conventional Ikeda and Mackey-Glass models, such as chaotic breathers, one-delay periodic motions, and chimera states.

The talk will first introduce the experimental and physical origins of the integro-differential delay model. Its specific dynamics will then be reported, with a special emphasis on the chimera states which we have been recently investigating for delay systems, and we will conclude with a short presentation of a recent application of delay dynamics exploiting the infinite dimensional phase and demonstrating a hardware implementation of a novel brain-inspired information processing concept known as Reservoir Computing, Echo State Network, Liquid State Machine, and also nonlinear transient computing.

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