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Bifurcation Diagrams Of Quadratic Differentials
, 1996
"... We study the versal deformations of quadratic differential z m+1 dz 2 and the bifurcation diagrams of trajectories therein, that is the set of parameters for which homoclinic vertical or horizontal trajectory exists. ..."
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We study the versal deformations of quadratic differential z m+1 dz 2 and the bifurcation diagrams of trajectories therein, that is the set of parameters for which homoclinic vertical or horizontal trajectory exists.
Smoothness properties of bifurcation diagrams
 Publ. Matemàtiques
, 1997
"... Strata of bifurcation sets related to the nature of the singular points or to connections between hyperbolic saddles in smooth families of planar vector fields, are smoothly equivalent to subanalytic sets. But it is no longer true when the bifurcation is related to transition near singular points, ..."
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properties. 1. Structures of bifurcation diagrams Let Xλ be a smooth (C∞) unfolding of planar vector fields, with parameter λ ∈ Rk. In the parameter space Rk, the bifurcation diagram Σ is the set on which one has a variation of the topological type of Xλ, and inversely Xλ is structurally stable for λ ∈ Rk
Bifurcation Diagrams for the Formation of Wrinkles
"... Subject to compression, elastic materials may undergo bifurcation of various kinds. A homogeneous material forms creases, whereas a bilayer consisting of a stiff film and a compliant substrate forms wrinkles. Here, we show several new types of bifurcation behavior for bilayers consisting of films ..."
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Subject to compression, elastic materials may undergo bifurcation of various kinds. A homogeneous material forms creases, whereas a bilayer consisting of a stiff film and a compliant substrate forms wrinkles. Here, we show several new types of bifurcation behavior for bilayers consisting of films
Bifurcation Diagrams of Nonlinear RLC Electrical Circuits
"... This work investigates the application of bifurcation diagrams in the chaotic study of nonlinear RLC electrical circuits. The relevant second order differential equations were solved for ranges of appropriate parameters using RungeKutta approach. The solutions obtained were employed to produce bifu ..."
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This work investigates the application of bifurcation diagrams in the chaotic study of nonlinear RLC electrical circuits. The relevant second order differential equations were solved for ranges of appropriate parameters using RungeKutta approach. The solutions obtained were employed to produce
bifurcation diagrams for highly nonlinear
"... Application of the parametric representation method to construct ..."
Bifurcation Diagrams of Population Models with Nonlinear Diffusion
 Jour. Comp. Appl. Math
, 2006
"... We develop analytical and numerical tools for the equilibrium solutions of a class of reactiondiffusion models with nonlinear diffusion rates. Such equations arise from population biology and material sciences. We obtain global bifurcation diagrams for various nonlinear diffusion functions and seve ..."
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Cited by 3 (2 self)
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We develop analytical and numerical tools for the equilibrium solutions of a class of reactiondiffusion models with nonlinear diffusion rates. Such equations arise from population biology and material sciences. We obtain global bifurcation diagrams for various nonlinear diffusion functions
Bifurcation diagrams and heteroclinic networks of octagonal hplanforms
 Journal of Nonlinear Science
, 2012
"... This paper completes the classification of bifurcation diagrams for Hplanforms in the Poincaré disc D whose fundamental domain is a regular octagon. An Hplanform is a steady solution of a PDE or integrodifferential equation in D, which is invariant under the action of a lattice subgroup Γ of U(1, ..."
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Cited by 7 (6 self)
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This paper completes the classification of bifurcation diagrams for Hplanforms in the Poincaré disc D whose fundamental domain is a regular octagon. An Hplanform is a steady solution of a PDE or integrodifferential equation in D, which is invariant under the action of a lattice subgroup Γ of U(1
BIFURCATIONAL DIAGRAM AND DISCRIMINANT OF COMPLETELY INTEGRABLE SYSTEM
"... In first part of this work we consider the set of polynomial first integrals f1,..., fn, which defines the bifurcational diagram Σ, and offer method how to construct new polynomial integral Φ, such as Σ ∈ {Φ = 0}. We prove that, if we take this new integral instead of the old one, new bifurcational ..."
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In first part of this work we consider the set of polynomial first integrals f1,..., fn, which defines the bifurcational diagram Σ, and offer method how to construct new polynomial integral Φ, such as Σ ∈ {Φ = 0}. We prove that, if we take this new integral instead of the old one, new bifurcational
Bifurcation Diagram of the Generalized 4th Appelrot Class
, 2005
"... The article continues the author’s publication in [Mech. Tverd. Tela, No. 34, 2004], in which the generalizations of the Appelrot classes of the Kowalevski top motions are found for the case of the double force field. We consider the analogue of the 4th Appelrot class. The trajectories of this famil ..."
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Cited by 2 (2 self)
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of this family fill the surface which is fourdimensional in the neighborhood of its generic points. The complete system of two integrals is pointed out. For these integrals the bifurcation diagram is established and the admissible region for the corresponding constants is found. 1
Results 1  10
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747