Bifurcations in Continuous Piecewise Linear Differential Systems
Applications to Low-Dimensional Electronic Oscillators
Springer
ISBN 978-3-031-21137-9
Standardpreis
Bibliografische Daten
Fachbuch
Buch. Softcover
2023
1 s/w-Abbildung.
In englischer Sprache
Umfang: xv, 311 S.
Format (B x L): 15,5 x 23,5 cm
Gewicht: 504
Verlag: Springer
ISBN: 978-3-031-21137-9
Weiterführende bibliografische Daten
Das Werk ist Teil der Reihe: RSME Springer Series
Produktbeschreibung
The work is divided into three parts. The first part motivates the study of PWL differential systems as the natural next step towards dynamic complexity when starting from linear differential systems. The nomenclature and some general results for PWL systems in arbitrary dimensions are introduced. In particular, a minimal representation of PWL systems, called canonical form, is presented, as well as the closing equations, which are fundamental tools for the subsequent study of periodic orbits.
The second part contains some results on PWL systems in dimension 2, both continuous and discontinuous, and both with two or three regions of linearity. In particular, the focus-center-limit cycle bifurcation and the Hopf-like bifurcation are completely described. The results obtained are then applied to the study of different electronic devices.
In the third part, several results on PWL differential systems in dimension 3 are presented. In particular, the focus-center-limit cycle bifurcation is studied in systems with two and three linear regions, in the latter case with symmetry. Finally, the piecewise linear version of the Hopf-pitchfork bifurcation is introduced. The analysis also includes the study of degenerate situations. Again, the above results are applied to the study of different electronic oscillators.
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A unique approach to piecewise linear (PWL) differential systems The bifurcation of periodic orbits is unveiled Including comprehensive analysis of some electronic oscillators
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