Abstract
AbstractNumerical continuation tools are nowadays standard methods for the bifurcation analysis of dynamical systems. Unfortunately, the full power of these methods is still unavailable in experiments, in particular, if no underlying mathematical model is at hand. We here aim to narrow this gap by providing control based continuation of periodic states which can be ultimately implemented in real-world experimental set-ups. Taking inspiration from atomic force microscopy, we develop experimentally relevant control and tracking tools for time periodic solutions in driven nonlinear oscillator systems based on stroboscopic maps.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Electrical and Electronic Engineering,Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Control and Systems Engineering
Reference42 articles.
1. Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991)
2. Karhunen, K.: Über lineare Methoden in der Wahrscheinlichkeitsrechnung, Ann. Acad. Sci. Fennicae Ser. A. I. Math.-Phys. 37, (1947)
3. Kantz, H., Schreiber, T.: Nonlinear Time Series Analysis. Cambridge University Press, Cambridge (1997)
4. Artuso, R., Aurell, E., Cvitanović, P.: Recycling of strange sets. Nonlinear 3, 325 (1990)
5. Krauskopf, B., Osinga, H., Galán-Vioque, J.: Numerical Continuation Methods for Dynamical Systems. Springer, Dordrecht (2007)
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