Recent investigations on the bifurcation behavior of power electronic dc-dc converters has revealed that most of the observed bifurcations do not belong to generic classes like saddle-node, period doubling or Hopf bifurcations. Since these systems yield piecewise smooth maps under stroboscopic sampling, a new class of bifurcations occur in such systems when a xed point crosses the \border" betw...

In this paper we show the homoclinic bifurcations which are involved in some contact bifurcations of basins of attraction in noninvertible two-dimensional map. That is, we are interested in the link between contact bifurcations of a chaotic area and homoclinic bifurcations of a saddle point or of an expanding fixed point located on the boundary of the basin of attraction of the chaotic area. We...

Thyristor controlled reactors are high power switching circuits used for static VAR control and the emerging technology of flexible ac transmission. The static VAR control circuit considered in the paper is a nonlinear periodically operated RLC circuit with a sinusoidal source and ideal thyristors with equidistant firing pulses. This paper describes new instabilities in the circuit in which thy...

The results of optimality studies of the branching angles of arterial bifurcations are extended to nonsymmetrical bifurcations. Predicted nonsymmetrical bifurcations are found to be not unlike those observed in the cardiovascular system.

After a short presentation of the boundary layer method extended to strongly elongated objects by Andronov and Bouche [1], the author develops some techniques for deriving explicit formulas for the asymptotic currents on a strongly elongated object of revolution excited by an electromagnetic plane wave propagating in the paraxial direction. The performance of the different techniques are demons...

We analyze the transition from annihilation to preservation of colliding waves. The analysis exploits the similarity between the local and global phase portraits of the system. The transition is shown to be the infinite-dimensional analog of the creation and annihilation of limit cycles in the plane via a homoclinic Andronov bifurcation, and has parallels to the nucleation theory of first-order...

Recently physical and computer experiments involving systems describable by continuous maps that are nondi8'erentiable on some surface in phase space have revealed novel bifurcation phenomena. These phenomena are part of a rich new class of bifurcations which we call border collisi-on bifurcations A. general criterion for the occurrence of border-collision bifurcations is given. Illustrative nu...

We give an overview of all codim 1 bifurcations in generic planar discontinuous piecewise smooth autonomous systems, here called Filippov systems. Bifurcations are defined using the classical approach of topological equivalence. This allows the development of a simple geometric criterion for classifying sliding bifurcations, i.e. bifurcations in which some sliding on the discontinuity boundary ...

We investigate dynamical system having a special structure namely a codimension-one invariant manifold that is preserved under the variation of parameters. We derive conditions such that bifurcations of codimension-one and of codimension-two occur in the system. The normal forms of these bifurcations are derived explicitly. Both local and global bifurcations are analysed and yield the transcrit...

We consider examples of loss of stability of chaotic attractors in invariant subspaces (blowouts) that occur on varying two parameters, i.e. codimension two blowout bifurca-tions. Such bifurcations act as organising centres for nearby codimension one behaviour, analogous to the case for codimension two bifurcations of equilibria. We consider examples of blowout bifurcations showing change of cr...