caa a22 4500 477037097 CHVBK 20180405111308.0 cr unu---uuuuu 170330e19960901xx s 000 0 eng 10.1007/BF02440161 doi (NATIONALLICENCE)springer-10.1007/BF02440161 Micro-chaos in digital control [Elektronische Daten] [G. Haller, G. Stépán] Summary: In this paper we analyze a model for the effect of digital control on one-dimensional, linearly unstable dynamical systems. Our goal is to explain the existence of small, irregular oscillations that are frequently observed near the desired equilibrium. We derive a one-dimensional map that captures exactly the dynamics of the continuous system. Using thismicro-chaos map, we prove the existence of a hyperbolic strange attractor for a large set of parameter values. We also construct an "instability chart” on the parameter plane to describe how the size and structure of the chaotic attractor changes as the parameters are varied. The applications of our results include the stick-and-slip motion of machine tools and other mechanical problems with locally negative dissipation. Springer-Verlag New York Inc., 1996 Haller G. Division of Applied Mathematics, Box F, Brown University, 02912, Providence, RI, USA aut Stépán G. Department of Applied Mechanics, Technical University of Budapest, H-1521, Budapest, Hungary aut Journal of Nonlinear Science Springer-Verlag 6/5(1996-09-01), 415-448 0938-8974 6:5<415 1996 6 332 https://doi.org/10.1007/BF02440161 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02440161 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Haller G. Division of Applied Mathematics, Box F, Brown University, 02912, Providence, RI, USA aut NATIONALLICENCE 700 1- Stépán G. Department of Applied Mechanics, Technical University of Budapest, H-1521, Budapest, Hungary aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 6/5(1996-09-01), 415-448 0938-8974 6:5<415 1996 6 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer