Forced oscillations and bifurcations

By Floris Takens. 2001

230 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Control and Systems Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/deb4a7521d5b5cb362dc9def4bb4b3ff2829df83

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In Civil and Structural Engineering

In Control and Systems Engineering

In Mechanics of Materials

Citations in the corpus

Bifurcation analysis of a class of first-order nonlinear delay-differential equations with reflectional symmetry (2002, background): “It is well-known[25] that the normal forms for the Takens–Bogdanov singularity with reflectional symmetry are determined to cubic order and are given by d dt z1 = z2, d dt z2 = az(3)1 + bz(2)1z2, (4.”
Global Analysis in a Predator-Prey System with Nonmonotonic Functional Response (2001, background): “Even though we can prove that the unique degenerate interior equilibrium E∗ is a cusp of codimension 2 and the system exhibits a Bogdanov–Takens bifurcation (see Bogdanov [4, 5] and Takens [33]), it is possible that system (1.”
Codimension-two bifurcation analysis in two-dimensional Hindmarsh–Rose model (2012, methodology): “The classification and unfolding of the planar system having an equilibrium with two zero eigenvalues was done simultaneously (and independently) by Bogdanov [11] and Takens [12, 13], i.”
Homoclinic and heteroclinic bifurcations in vector fields (2010, methodology): “This bifurcation was studied by Bogdanov [42] and Takens [388] (reproduced in [393]); a streamlined analysis can be found in [332].”
Hopf saddle-node bifurcation for fixed points of 3D-diffeomorphisms: Analysis of a resonance ‘bubble’ (2008, methodology): “Given a family of diffeomorphisms Fα , α ∈ Rp, a standard approach for the study of a bifurcation of fixed points of Fα consists in the analysis of the Takens normal form vector field, see [61] and Appendix A.”