

Artikel
Bifurcations in Nonsmooth Dynamical Systems
Författare: 
di Bernardo, M., Budd, C J, Champneys, A. R. , Kowalczyk, P., Nordmark, A., Olivar, G., Piiroinen, P T 
Dokumenttyp: 
Artikel 
Tillstånd: 
Publicerad 
Tidskrift: 
SIAM Review 
Volym: 
50(4)
629701 
År: 
2008 
AbstractA review is presented of the oneparameter, nonsmooth bifurcations that occur in a variety of continuoustime piecewisesmooth dynamical systems. Motivated by applications, a pragmatic approach is taken to defining a discontinuityinduced bifurcation (DIB) as a nontrivial interaction of a limit set with respect to a codimensionone discontinuity boundary in phase space. Only DIBs that are local are considered, that is, bifurcations involving equilibria or a single point of boundary interaction along a limit cycle for flows. Three classes of systems are considered, involving either state jumps, jumps in the vector field, or jumps in some derivative of the vector field. A rich array of dynamics are revealed, involving the sudden creation or disappearance of attractors, jumps to chaos, bifurcation diagrams with sharp corners, and cascades of period adding. For each kind of bifurcation identified, where possible, a kind of “normal form” or discontinuity mapping (DM) is given, together with a canonical example and an application. The goal is always to explain dynamics that may be observed in simulations of systems which include friction oscillators, impact oscillators, DCDC converters, and problems in control theory.

