A REMARK ON HETEROCLINIC BIFURCATIONS NEAR STEADY STATE/PITCHFORK BIFURCATIONS

DOI10.1142/S0218127404011752zbMath1090.37553MaRDI QIDQ5474140

Vivien Kirk, Edgar Knoblauch

Publication date: 23 June 2006

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

heteroclinic bifurcationsaddle-node/Hopf bifurcationnonhyperbolic fixed pointssteady state/heteroclinic bifurcation

Mathematics Subject Classification ID

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)

Cites Work

• Unnamed Item
• Pitchfork bifurcation with a heteroclinic orbit: Normal form, recognition criteria, and universal unfolding
• \(C^ p\) singularity theory and heteroclinic bifurcation with a distinguished parameter
• Local and global bifurcations at infinity in models of glycolytic oscillations
• Periodic and Steady-State Mode Interactions Lead to Tori
• Simultaneous equilibrium and heteroclinic bifurcation of planar vector fields via the Melnikov integral
• Natural doubly diffusive convection in three-dimensional enclosures
• The Saddle-Node Separatrix-Loop Bifurcation
• Codimension-three unfoldings of reflectionally symmetric planar vector fields
• Nonlinear dynamics in Langmuir circulations with O(2) symmetry
• A three-parameter study of a degenerate case of the Hopf-pitchfork bifurcation
• ON A CODIMENSION-THREE UNFOLDING OF THE INTERACTION OF DEGENERATE HOPF AND PITCHFORK BIFURCATIONS
• Finite-Dimensional Dynamics in Taylor-Couette Flow