Interplay between Normal Forms and Center Manifold Reduction for Homoclinic Predictors near Bogdanov–Takens Bifurcation
DOI10.1137/22m151354xarXiv2109.12570WikidataQ129379321 ScholiaQ129379321MaRDI QIDQ6192106
Maikel Bosschaert, Yuri A. Kuznetsov
Publication date: 12 February 2024
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2109.12570
Nonlinear boundary value problems for ordinary differential equations (34B15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Parameter dependent boundary value problems for ordinary differential equations (34B08) Computational methods for bifurcation problems in dynamical systems (37M20) Numerical bifurcation problems (65P30) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Boundary value problems on infinite intervals for ordinary differential equations (34B40) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)
Cites Work
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- A hyperbolic Lindstedt-Poincaré method for homoclinic motion of a kind of strongly nonlinear autonomous oscillators
- Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems
- Homoclinic and heteroclinic solutions of cubic strongly nonlinear autonomous oscillators by hyperbolic Lindstedt-Poincaré method
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Numerical methods in bifurcation problems. Lectures delivered at the Indian Institute of Science, Bangalore, under the T.I.F.R.-I.I.Sc. Programme in Applications of Mathematics. Notes by A. K. Nandakumaran and Mythily Ramaswamy
- Versal deformation of a singular point of a vector field on the plane in the case of zero eigenvalues
- A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens-Bogdanov normal form
- Generalized hyperbolic perturbation method for homoclinic solutions of strongly nonlinear autonomous systems
- Homoclinic and heteroclinic solutions of cubic strongly nonlinear autonomous oscillators by the hyperbolic perturbation method
- Initialization of Homoclinic Solutions near Bogdanov--Takens Points: Lindstedt--Poincaré Compared with Regular Perturbation Method
- Julia: A Fresh Approach to Numerical Computing
- Improved Homoclinic Predictor for Bogdanov–Takens Bifurcation
- New features of the software M<scp>at</scp>C<scp>ont</scp>for bifurcation analysis of dynamical systems
- ANALYSIS AND IMPROVEMENT OF PERTURBATION SERIES
- Numerical Normalization Techniques for All Codim 2 Bifurcations of Equilibria in ODE's
- Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point
- Normal Forms and Unfoldings for Local Dynamical Systems
- Numerical Methods for Bifurcations of Dynamical Equilibria
- PRACTICAL COMPUTATION OF NORMAL FORMS ON CENTER MANIFOLDS AT DEGENERATE BOGDANOV–TAKENS BIFURCATIONS
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