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Global dynamics of delay differential equations

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Abstract

In this survey paper the delay differential equation \( \dot x(t) = - \mu x(t) + g(x(t - 1)) \)(t) = −µx(t) + g(x(t − 1)) is considered with µ ≥ 0 and a smooth real function g satisfying g(0) = 0. It is shown that the dynamics generated by this simple-looking equation can be very rich. The dynamics is completely understood only for a small class of nonlinearities. Open problems are formulated.

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Correspondence to Tibor Krisztin.

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Dedicated to the memory of Professor Miklós Farkas

Supported in part by the Hungarian NFSR, Grant No. T049516.

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Krisztin, T. Global dynamics of delay differential equations. Period Math Hung 56, 83–95 (2008). https://doi.org/10.1007/s10998-008-5083-x

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  • DOI: https://doi.org/10.1007/s10998-008-5083-x

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