Intermittency and Jakobson’s theorem near saddle-node bifurcations

Intermittency and Jakobson's theorem near saddle-node bifurcations

Jakobson’s Theorem near saddle-node bifurcations

We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node bifurcation. It was previously shown that for a parameter set of positive Lebesgue density at the bifurcation, the maps possess attracting periodic orbits of high period. We show that there is also a parameter set of positive density at the bifurcation, for which the maps exhibit abs...

Intermittency in families of unimodal maps

We consider intermittency in one parameter families of unimodal maps, induced by saddle node and boundary crisis bifurcations. In these bifurcations a periodic orbit or a periodic interval, respectively, disappears to give rise to chaotic bursts. We prove asymptotic formulae for the frequency with which orbits visit the region previously occupied by the attractor. For this, we extend results of...

Bifurcation structure of a model of bursting pancreatic cells.

One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic beta-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other. The transition from this structure to the so-called period-adding structure is found to involve a subcritica...

Hopf-saddle-node bifurcation for fixed points of 3D-diffeomorphisms: analysis of a resonance ‘bubble’

The dynamics near a Hopf-saddle-node bifurcation of fixed points of diffeomorphisms is analysed by means of a case study: a two-parameter model map G is constructed, such that at the central bifurcation the derivative has two complex conjugate eigenvalues of modulus one and one real eigenvalue equal to 1. To investigate the effect of resonances, the complex eigenvalues are selected to have a 1:...