A Global Analysis of the Bogdanov–Takens System
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Publication:4018873
DOI10.1137/0152069zbMath0758.58026OpenAlexW2018058302MaRDI QIDQ4018873
Publication date: 16 January 1993
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0152069
Bifurcation theory for ordinary differential equations (34C23) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Local and nonlocal bifurcation theory for dynamical systems (37G99)
Related Items (16)
A proof of Perko's conjectures for the Bogdanov-Takens system ⋮ A proof of Wang-Kooij's conjectures for a cubic Liénard system with a cusp ⋮ Bifurcation diagram and global phase portraits of a family of quadratic vector fields in class \(I\) ⋮ An improvement of the non-existence region for limit cycles of the Bogdanov-Takens system ⋮ Controllability near Takens-Bogdanov points ⋮ Chaos of liquid surface waves in a vessel under vertical excitation with slowly modulated amplitude ⋮ Global phase portrait of a degenerate Bogdanov-Takens system with symmetry ⋮ HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS ⋮ Global bifurcation studies of a cubic Liénard system ⋮ Global phase portraits of a degenerate Bogdanov-Takens system with symmetry. II ⋮ Homoclinic Loop and Multiple Limit Cycle Bifurcation Surfaces ⋮ Bifurcation diagram and stability for a one-parameter family of planar vector fields ⋮ A nonlinear time transformation method to compute all the coefficients for the homoclinic bifurcation in the quadratic Takens-Bogdanov normal form ⋮ Complete bifurcation diagram and global phase portraits of Liénard differential equations of degree four ⋮ Limit cycles and homoclinic orbits and their bifurcation of Bogdanov-Takens system ⋮ Bifurcation of the separatrix skeleton in some 1-parameter families of planar vector fields
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