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Bifurcation Diagram of a Map with Multiple Critical Points
International Journal of Bifurcation and Chaos, 2018In this work a conjecture to draw the bifurcation diagram of a map with multiple critical points is enunciated. The conjecture is checked by using two quartic maps in order to verify that the bifurcation diagrams obtained according to the conjecture contain all the periodic orbits previously counted by Xie and Hao for maps with four laps.
M. Romera +7 more
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Counting Central Configurations at the Bifurcation Points
Acta Applicandae Mathematicae, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Bifurcation Points on the Maclaurin Sequence
Publications of the Astronomical Society of Japan, 1984Abstract All bifurcation points on the Maclaurin spheroidal sequence are calculated. Deformation types can be expressed by associated Legendre functions, i.e., Pnmηcos mϕ..
Izumi Hachisu, Yoshiharu Eriguchi
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Computation of multiple bifurcation point
Engineering Computations, 2006PurposeThe aim of this paper is to develop a new method for finding multiple bifurcation points in structures.Design/methodology/approachA brief review of nonlinear analysis is presented. A powerful method (called arc‐length) for tracing nonlinear equilibrium path is described.
M. Rezaiee‐Pajand +1 more
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Bifurcation points of Hammerstein equations
Integral Equations and Operator Theory, 1993We apply global bifurcation theorems to systems of nonlinear integral equations of Hammerstein type involving a scalar parameter. To this end, we give sufficient conditions for the continuous dependence, compactness, Fréchet differentiability, and asymptotic linearity of the corresponding operators, which are more general than in the classical setting.
Appell, Jürgen, Zabrejko, Petr P.
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The homoclinic twist bifurcation point
1992We analyze bifurcations occurring in the vicinity of a homoclinic twist point for a generic two parameter family of Z 2 equivariant ODE’s in four dimensions. The results are compared with numerical results for a system of two coupled Josephson junctions with pure capacitive load.
Aronson, D.G., van Gils, S.A., Krupa, M.
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A Postprocessing of Hopf Bifurcation Points
2004The aim is to initialize a branch of periodic orbits emanating from a Hopf bifurcation point. The second-order predictor of the branch is developed. The problem is discussed in the context of the MATLAB toolbox CL_MATCONT.
Dáša Janovská, Vladimír Janovský
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Bifurcations of periodic points
1979This thesis was prepared at the Rijksuniversiteit Groningen during the years 1974 - 1979. In it we consider the behaviour of periodic points in r-parameter families of diffeomorphisms. A more precise formulation may be found in chapter I (the introduction). There also the content of the various chapters is described.
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Detecting and Computing Bifurcation Points
2000Exploring nonlinear phenomena has become a major challenge in physics, chemistry, biology, engineering, medicine and social science. We consider nonlinear problems of the form $$\frac{{\partial u}}{{\partial t}} = G(u,\lambda ) $$ (3.1) where G : X x R p → Y is a “smooth” mapping and λ ∈ R p represents various control parameters, e.g ...
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Humankind and the World at the Point of Bifurcation
Russian Journal of Philosophical SciencesThe article examines the developmental prospects of civilization from the perspective of self-organization theory and synergetics, which are becoming foundational for understanding the processes of the 21st century. The author argues that the contemporary world is at a bifurcation point, characterized by a loss of stability in its previous ...
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