The dynamics of mechanical systems with dry friction is affected by non-smooth bifurcations, which have been recently partially classified as ‘sliding bifurcations’. In applied science a bifurcation is usually seen as the point in which the number of fixed points and/or (quasi-)periodic solutions changes. The paper describes with several detailed examples that ‘sliding bifurcations’ do not alwa...

This paper is devoted to the analysis of bifurcations in a three-parameter unfolding of a linear degeneracy corresponding to a triple-zero eigenvalue. We carry out the study of codimensiontwo local bifurcations of equilibria (Takens–Bogdanov and Hopf-zero) and show that they are nondegenerate. This allows to put in evidence the presence of several kinds of bifurcations of periodic orbits (secon...

In this article, we study the nonlinear dynamics of a quadratic system in the three dimensional space which can be obtained from a scalar third order differential equation. More precisely, we study the stability and bifurcations which occur in a parameter dependent quadratic system in the three dimensional space. We present an analytical study of codimension one, two and three Hopf bifurcations...

By using a non linear discrete time model, this paper shows how to predict bifurcations in a two cells chopper and analyses the road to chaos. Equilibrium points and their stability are investigated in an analogical way to determine the nature of the bifurcations. The global behaviour is studied by using bifurcation diagrams showing collisions between fixed points and borderlines. The border co...

Title of Dissertation: LOW DIMENSIONAL CHAOS: PHASE SYNCHRONIZATION AND INDETERMINATE BIFURCATIONS Romulus Breban, Doctor of Philosophy, 2003 Dissertation directed by: Professor Edward Ott Department of Physics We address two problems of both theoretical and practical importance in dynamical systems: Phase Synchronization of Chaos in the Presence of Two Competing Periodic Signals, and Saddle-No...

The geometry of natural branching systems generally reflects functional optimization. A common property is that their bifurcations are planar and that daughter segments do not turn back in the direction of the parent segment. The present study investigates whether this also applies to bifurcations in 3D dendritic arborizations. This question was earlier addressed in a first study of flatness of...

A system of two ordinary differential equations is proposed to model chemically-mediated interactions between plants and herbivores by incorporating a toxin-modifiednumerical response. This numerical response accounts for the reduction in her-bivore's growth reproduction due chemical defenses from plants. It shownthat exhibits very rich dynamics including saddle-node bifurcations, Hopfbifurcati...

The dynamical bifurcations of a laser with a saturable absorber were calculated, with the 3-2 level model, as function of the gain parameter. The average power of the laser is shown to have specific behavior at bifurcations. The succession of periodic-chaotic windows, known to occur in the homoclinic chaos, was studied numerically. A critical exponent of 1/2 is found on the tangent bifurcations...

A discontinuous change in the size of an attractor is the most easily observed type of global bifurcation. More generally, an explosion is a discontinuous change in the set of recurrent points. An explosion often results from heteroclinic and homoclinic tangency bifurcations. We prove that, for one-dimensional maps, explosions are generically the result of either tangency or saddle-node bifurca...