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Structure in the bifurcation diagram of the Duffing oscillator
Physical Review E, 1995We identify four levels of structure in the bifurcation diagram of the two-well periodically driven Duffing oscillator, plotted as a function of increasing control parameter T, the period of the driving term. The superstructure, or bifurcation peninsula, repeats periodically as T increases by \ensuremath{\sim}2\ensuremath{\pi}, beginning and ending ...
Robert Gilmore, J. W. L. McCallum
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Bifurcation diagram for a piecewise-linear circuit [PDF]
IEEE Transactions on Circuits and Systems, 1984 The bifurcation diagram of an R-L -Diode circuit driven by a sinusoidal voltage source is computed. The model of the diode is piecewise linear. Qualitatively, the same phenomena have been obtained as for the previously published computer simulation with the conventional junction diode model.
R. Duhr, Martin Hasler, A. Azzouz
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VISUALIZING BIFURCATIONS IN HIGH DIMENSIONAL SYSTEMS: THE SPECTRAL BIFURCATION DIAGRAM
International Journal of Bifurcation and Chaos, 2003This paper presents methods to visualize bifurcations in flows of nonlinear dynamical systems, using the Lorenz '96 systems as examples. Three techniques are considered; the first two, density and max/min diagrams, are analagous to the bifurcation diagrams used for maps, which indicate how the system's behavior changes with a control parameter ...
David Orrell +3 more
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Physica Scripta, 2023
In this paper, the behavior of a 1D chaotic map is proposed which includes two sine terms and shows unique dynamics. By varying the bifurcation parameter, the map has a shift, and the system’s dynamics are generated around the cross points of the map and
Janarthanan Ramadoss +5 more
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In this paper, the behavior of a 1D chaotic map is proposed which includes two sine terms and shows unique dynamics. By varying the bifurcation parameter, the map has a shift, and the system’s dynamics are generated around the cross points of the map and
Janarthanan Ramadoss +5 more
semanticscholar +1 more source
A Simple Guide for Plotting a Proper Bifurcation Diagram
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2021In this paper, we propose a guideline for plotting the bifurcation diagrams of chaotic systems. We discuss numerical and mathematical facts in order to obtain more accurate and more elegant bifurcation diagrams.
A. Jafari +4 more
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Computing 3D Bifurcation Diagrams [PDF]
AIP Conference Proceedings, 2008 The nature and localization of critical parameter sets called bifurcations is a central issue in nonlinear dynamical system theory. Codimension‐1 bifurcations form hypersurfaces in parameter space. Some bifurcations of higher codimension can be identified as intersections of these surfaces.
D. Stiefs +3 more
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Qualitative bifurcation diagrams
Expert Systems, 2013AbstractWe explore the use of qualitative reasoning to predict the behaviour of a dynamical system given a change in one of its parameters based upon a qualitative representation of its bifurcation diagram. We present three algorithms to perform this task.
Andrzej Proskurowski +3 more
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