TY  - BOOK
AU  - Laurea,Mario di Bernardo
AU  - Champneys,Alan R.
AU  - Budd,Christopher J.
AU  - Kowalczyk,Piotr
ED  - SpringerLink (Online service)
TI  - Piecewise-smooth Dynamical Systems: Theory and Applications 
T2  - Applied Mathematical Sciences,
SN  - 9781846287084
AV  - QA299.6-433 
U1  - 515 23
PY  - 2008///
CY  - London
PB  - Springer London
KW  - Mathematics
KW  - Mathematical analysis
KW  - Analysis (Mathematics)
KW  - Dynamics
KW  - Ergodic theory
KW  - Applied mathematics
KW  - Engineering mathematics
KW  - Vibration
KW  - Dynamical systems
KW  - Control engineering
KW  - Robotics
KW  - Mechatronics
KW  - Electrical engineering
KW  - Analysis
KW  - Dynamical Systems and Ergodic Theory
KW  - Control, Robotics, Mechatronics
KW  - Vibration, Dynamical Systems, Control
KW  - Electrical Engineering
KW  - Applications of Mathematics
N1  - Qualitative theory of non-smooth dynamical systems -- Border-collision in piecewise-linear continuous maps -- Bifurcations in general piecewise-smooth maps -- Boundary equilibrium bifurcations in flows -- Limit cycle bifurcations in impacting systems -- Limit cycle bifurcations in piecewise-smooth flows -- Sliding bifurcations in Filippov systems -- Further applications and extensions
N2  - Traditional analysis of dynamical systems has restricted its attention to smooth problems, but it has become increasingly clear that there are distinctive phenomena unique to discontinuous systems that can be analyzed mathematically but which fall outside the usual methodology for smooth dynamical systems. The primary purpose of this book is to present a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction asserts the ubiquity of such models with examples drawn from mechanics, electronics, control theory and physiology. The main thrust is to classify complex behavior via bifurcation theory in a systematic yet applicable way. The key concept is that of a discontinuity-induced bifurcation, which generalizes diverse phenomena such as grazing, border-collision, sliding, chattering and the period-adding route to chaos. The results are presented in an informal style and illustrated with copious examples, both theoretical and experimental. Aimed at a wide audience of applied mathematicians, engineers and scientists at the early postgraduate level, the book assumes only the standard background of basic calculus and linear algebra for most of the presentation and will be an indispensable resource for students and researchers. The inclusion of a comprehensive bibliography and many open questions will also serve as a stimulus for future research
UR  - http://dx.doi.org/10.1007/978-1-84628-708-4
ER  -