Bifurcation diagram

About: Bifurcation diagram is a research topic. Over the lifetime, 8379 publications have been published within this topic receiving 139664 citations.

Multistability and memory effect in a highly turbulent flow: experimental evidence for a global bifurcation.

Abstract: We report an experimental evidence of a global bifurcation on a highly turbulent von Karman flow. The mean flow presents multiple solutions: the canonical symmetric solution becomes marginally unstable towards a flow which breaks the basic symmetry of the driving apparatus even at very large Reynolds number. The global bifurcation between these states is highly subcritical and the system thus keeps a memory of its history. The transition recalls low-dimension dynamical systems transitions and exhibits a very peculiar statistics. We discuss the role of turbulence in two ways: the multiplicity of hydrodynamical solutions and the effect of fluctuations on the nature of transitions.

Study of bifurcations in current-programmed DC/DC boost converters: from quasiperiodicity to period-doubling

Abstract: This paper studies the bifurcation paths exhibited by a simple second-order DC/DC boost converter under current-programmed control with and without voltage feedback. Previous work in this area has reported two distinct types of bifurcation paths, namely via regions of quasi-periodic orbits and period-doubling. This paper demonstrates that the two different types of bifurcation paths can, in fact, be viewed as part of another bifurcation in which the quasi-periodic sequence transmutes into the period-doubling sequence, and that such a bifurcation is observed regardless of the presence of the outer voltage feedback loop as long as a suitable set of bifurcation parameters is chosen. The describing iterative map is derived in closed form and is used to develop the main results via a series of computer experiments. The characteristic multipliers are calculated and the first onset of flip-bifurcation is predicted. Computer simulation based on an exact piecewise switched model confirms the predicted bifurcations. The exhibition of quasi-periodic orbits is confirmed by computation of the Lyapunov exponent. Finally, a series of return maps are generated to provide an alternative viewpoint to the reported bifurcations in terms of a transmutation from a tent-like map to a logistic-like map.

The Hindmarsh-Rose neuron model: bifurcation analysis and piecewise-linear approximations.

Abstract: This paper provides a global picture of the bifurcation scenario of the Hindmarsh–Rose model. A combination between simulations and numerical continuations is used to unfold the complex bifurcation structure. The bifurcation analysis is carried out by varying two bifurcation parameters and evidence is given that the structure that is found is universal and appears for all combinations of bifurcation parameters. The information about the organizing principles and bifurcation diagrams are then used to compare the dynamics of the model with that of a piecewise-linear approximation, customized for circuit implementation. A good match between the dynamical behaviors of the models is found. These results can be used both to design a circuit implementation of the Hindmarsh–Rose model mimicking the diversity of neural response and as guidelines to predict the behavior of the model as well as its circuit implementation as a function of parameters.