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Bifurcation analysis of a piecewise smooth system with non‐linear characteristics
Author(s) -
Kousaka Takuji,
Ueta Tetsushi,
Ma Yue,
Kawakami Hiroshi
Publication year - 2005
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.320
Subject(s) - piecewise linear function , bifurcation , mathematics , network analysis , piecewise , computer science , control theory (sociology) , mathematical analysis , calculus (dental) , nonlinear system , engineering , artificial intelligence , physics , control (management) , quantum mechanics , medicine , dentistry , electrical engineering
In previous works, there are no results about the bifurcation analysis for a piecewise smooth system with non‐linear characteristics. The main purpose of this study is to calculate the bifurcation sets for a piecewise smooth system with non‐linear characteristics. We first propose a new method to track the bifurcation sets in the system. This method derives the composite discrete mapping, Poincaré mapping. As a result, it is possible to obtain the local bifurcation values in the parameter plane. As an illustrated example, we then apply this general methodology to the Rayleigh‐type oscillator containing a state‐ period‐dependent switch. In the circuit, we can find many subharmonic bifurcation sets including global bifurcations. We also show the bifurcation sets for the border‐collision bifurcations. Some theoretical results are verified by laboratory experiments. Copyright © 2005 John Wiley & Sons, Ltd.