Initialization of Homoclinic Solutions near Bogdanov--Takens Points: Lindstedt--Poincaré Compared with Regular Perturbation Method

DOI10.1137/15M1017491zbMath1343.34104OpenAlexW2398128155MaRDI QIDQ2812218

Yuri A. Kuznetsov, Hil G. E. Meijer, Willy Govaerts, Bashir Al-Hdaibat

Publication date: 16 June 2016

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1017491

zbMATH Keywords

homoclinic orbitsLindstedt-Poincaré methodregular perturbation methodBogdanov-Takens bifurcationMatCont

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Computational methods for bifurcation problems in dynamical systems (37M20) Numerical bifurcation problems (65P30) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (11)

Bifurcation analysis of a Kolmogorov type tritrophic model ⋮ Approximations of the Homoclinic Orbits Near a Double-Zero Bifurcation with Symmetry of Order Two ⋮ Interplay between Normal Forms and Center Manifold Reduction for Homoclinic Predictors near Bogdanov–Takens Bifurcation ⋮ Explicit transversality conditions and local bifurcation diagrams for bogdanov-Takens bifurcation on center manifolds ⋮ Bifurcations in a Cancer and Immune Model with Allee Effect ⋮ A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens-Bogdanov normal form ⋮ Switching to Nonhyperbolic Cycles from Codimension Two Bifurcations of Equilibria of Delay Differential Equations ⋮ Bautin bifurcation in a minimal model of immunoediting ⋮ Approximations of the Heteroclinic Orbits Near a Double-Zero Bifurcation with Symmetry of Order Two. Application to a Liénard Equation ⋮ Bifurcation analysis of an SIR model with logistic growth, nonlinear incidence, and saturated treatment ⋮ Remarks on homoclinic structure in Bogdanov-Takens map

Uses Software

• MATCONT
• Matlab
• HomCont

Cites Work

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