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Zbl 1079.37011
Peng, Mingshu
Symmetry breaking, bifurcations, periodicity and chaos in the Euler method for a class of delay differential equations. (English)
[J] Chaos Solitons Fractals 24, No. 5, 1287-1297 (2005). ISSN 0960-0779

The author proposes a discrete model to study the bifurcation and the chaotic behaviour of a class of delay differential equations (DDEs), which have a broad variety of applications and involve periodic nonlinearities with several zeroes. Analytical and numerical results for the discrete model, especially higher dimensions, are described. By considering the DDEs, rich dynamics of nonlinear delay differential systems can be studied, although the delay systems here only contains a nonlinear term depending on the variable.
[Messoud A. Efendiev (Berlin)]

MSC 2000:: *37C10 Vector fields, flows, ordinary differential equations
34K23 Complex (chaotic) behavior of solutions of FDE
34K18 Bifurcation theory of functional differential equations
34K13 Periodic solutions of functional differential equations

Keywords: rich dynamics; discrete model; delay differential equation; bifurcation; chaotic behaviour; periodic nonlinearities

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