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Modeling as a Means to Develop New Ideas: The Case of Reinventing a Bifurcation Diagram
PRIMUS - Problems, Resources, and issues in mathematics undergraduate studies, 2019This article provides an overview of a modeling sequence that culminates in student reinvention of a bifurcation diagram. The sequence is the result of years of classroom-based research and curriculum development grounded in the instructional design ...
C. Rasmussen +3 more
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Bifurcation diagram of coupled thermoacoustic chaotic oscillators.
Chaos, 2018A thermoacoustic chaotic oscillator is a fluid system that presents thermally induced chaotic oscillations of a gas column. This study experimentally reports a bifurcation diagram when two thermoacoustic chaotic oscillators are dissipatively coupled to ...
R. Delage, Y. Takayama, T. Biwa
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Bifurcation Diagram of a Map with Multiple Critical Points
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2018In this work a conjecture to draw the bifurcation diagram of a map with multiple critical points is enunciated.
M. Romera +7 more
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Geometry of bifurcation diagrams
Journal of Soviet Mathematics, 1984The geometry of a bifurcation diagram in the base of a versal deformation of a singularity is studied for single singularities on a manifold with boundary. In particular, vector fields and groups of diffeomorphisms are studied which are defined in a neighborhood of a bifurcation diagram as are stratification of a bifurcation diagram and decomposition ...
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Experimentally Observed Bifurcation Diagrams
2002Extensive studies of structures and materials undergoing perfect and imperfect bifurcation have been conducted. Bifurcation of structures can be highlighted, e.g., by Ziegler, 1968, 1977 [196]; Thompson and Hunt, 1973, 1984 [174], [175]; Ben-Haim and Elishakoff, 1990 [14]; Bažant and Cedolin, 1991 [12]; and references therein.
Kazuo Murota, Kiyohiro Ikeda
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Hero’s journey in bifurcation diagram
Communications in Nonlinear Science and Numerical Simulation, 2012Abstract The hero’s journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure.
P.N. Mustaro +2 more
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BIFURCATION DIAGRAM AND CONTROL OF LOCALIZED LASER STRUCTURES
, 2012We describe experimentally the bifurcation diagram of localized lasing states in a cavity soliton laser (CSL). The CSL is based on two coupled semiconductor microcavities, one providing gain and the other providing saturable absorption.
P. Genevet +4 more
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The Shadow-Curves of the Orbit Diagram Permeate the bifurcation Diagram, Too
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2009The "Q-curves have long been observed and studied as the shadowy curves which appear illusively — not explicitly drawn — in the familiar orbit diagram of Myrberg's map fc(x) = x2 + c.
C. Ross, M. Odell, Sarah Cremer
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On the bifurcation diagram of discrete analogues for ordinary bifurcation problems
Mathematical Methods in the Applied Sciences, 1979AbstractOrdinary bifurcation problems of the form (1) typically have at most one nontrivial, nonnegative solution for λ > 0. The paper shows that this is in general not true for discrete analogues to (1) no matter how small the step width h > 0 is chosen.
K. Kirchgassner, E. Bohl
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Bifurcation diagram and the discriminant of a?spectral curve of integrable systems on Lie algebras
, 2010A bifurcation diagram is a?stratified (in general, nonclosed) set and is one of the efficient tools of studying the topology of the Liouville foliation. In the framework of the present paper, the coincidence of the closure of a?bifurcation diagram of the
A. Konyaev
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