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• W2000862887 abstract "The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics, ranging from periodic solutions through to spatio-temporal chaos. In this paper, we consider a class of scalar partial differential equations with a delayed threshold nonlinearity which admits exact solutions for equilibria, periodic orbits and travelling waves. Importantly, we show how the spectra of periodic and travelling wave solutions can be determined in terms of the zeros of a complex analytic function. Using this as a computational tool to determine stability, we show that delays can have very different effects on threshold systems with negative as opposed to positive feedback. Direct numerical simulations are used to confirm our bifurcation analysis, and to probe some of the rich behaviour possible for mixed feedback." @default.
• W2000862887 created "2016-06-24" @default.
• W2000862887 creator A5001340107 @default.
• W2000862887 creator A5015605154 @default.
• W2000862887 date "2009-02-01" @default.
• W2000862887 modified "2023-10-18" @default.
• W2000862887 title "Instabilities in threshold-diffusion equations with delay" @default.
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• W2000862887 doi "https://doi.org/10.1016/j.physd.2008.10.014" @default.
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