Detection of periodic driving in nonautonomous difference equations. (English) Zbl 1179.65159

Sauer, Timothy

Elaydi, Saber (ed.) et al., Advances in discrete dynamical systems. Proceedings of the 11th international conference on difference equations and applications (ICDEA 06), Kyoto, Japan, July 24–28, 2006. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-49-5/hbk). Advanced Studies in Pure Mathematics 53, 301-309 (2009).

Summary: An algorithm is proposed for determining the periodic behavior of the common driver of a system of nonautonomous difference equations from observations of the equation trajectories only. Methods of attractor reconstruction are used to build a semiconjugacy to a topological version of the driver system. The algorithm is described in detail and implemented on several examples.
For the entire collection see [Zbl 1170.39300].

MSC:

65Q10	Numerical methods for difference equations
39A10	Additive difference equations
39A23	Periodic solutions of difference equations

Keywords:

numerical examples; periodic solutions; system identification; algorithm; system of nonautonomous difference equations; attractor reconstruction; semiconjugacy