Nontransversal curves of \(T\)-points: A source of closed curves of global bifurcations

DOI10.1016/S0375-9601(02)01256-2zbMath0999.37035OpenAlexW1979448288MaRDI QIDQ1847716

Fernando Fernández-Sánchez, Alejandro J. Rodríguez-Luis, Emilio Freire, Manuel Merino, Antonio Algaba

Publication date: 23 October 2002

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0375-9601(02)01256-2

zbMATH Keywords

heteroclinic connectionshomoclinic connectionsautonomous three-dimensional systems

Mathematics Subject Classification ID

Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (11)

OPEN-TO-CLOSED CURVES OF SADDLE-NODE BIFURCATIONS OF PERIODIC ORBITS NEAR A NONTRANSVERSAL T-POINT IN CHUA'S EQUATION ⋮ Using Lin's method to solve Bykov's problems ⋮ Analysis of the T-point-Hopf bifurcation in the Lorenz system ⋮ Dynamics Near the Heterodimensional Cycles with Nonhyperbolic Equilibrium ⋮ A model for the analysis of the dynamical consequences of a nontransversal intersection of the two-dimensional manifolds involved in a T-point ⋮ CLOSED CURVES OF GLOBAL BIFURCATIONS IN CHUA'S EQUATION: A MECHANISM FOR THEIR FORMATION ⋮ BI-SPIRALING HOMOCLINIC CURVES AROUND A T-POINT IN CHUA'S EQUATION ⋮ Analysis of the T-point-Hopf bifurcation ⋮ ANALYSIS OF THE T-POINT–HOPF BIFURCATION WITH ℤ₂-SYMMETRY: APPLICATION TO CHUA'S EQUATION ⋮ Symmetric periodic orbits near a heteroclinic loop in \(\mathbb R^3\) formed by two singular points, a semistable periodic orbit and their invariant manifolds ⋮ HOMOCLINIC INTERACTIONS NEAR A TRIPLE-ZERO DEGENERACY IN CHUA'S EQUATION

Uses Software

• AUTO
• HomCont

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• T-points: A codimension two heteroclinic bifurcation
• Hypernormal form calculation for triple-zero degeneracies
• Global bifurcations and chaos. Analytical methods
• Elements of applied bifurcation theory.
• The bifurcations of separatrix contours and chaos
• A case study for homoclinic chaos in an autonomous electronic circuit. A trip from Takens-Bogdanov to Hopf-Sil'nikov
• A tame degenerate Hopf-pitchfork bifurcation in a modified van der Pol-Duffing oscillator
• T-points in a \(\mathbb Z_2\)-symmetric electronic oscillator. I: Analysis
• The non-transverse Shil'nikov-Hopf bifurcation: uncoupling of homoclinic orbits and homoclinic tangencies
• Isolas, cusps and global bifurcations in an electronic oscillator
• A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation
• NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS
• TAKENS–BOGDANOV BIFURCATIONS OF PERIODIC ORBITS AND ARNOLD'S TONGUES IN A THREE-DIMENSIONAL ELECTRONIC MODEL

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