Bifurcations of heteroclinic loop accompanied by pitchfork bifurcation

DOI10.1007/s11071-012-0563-3zbMath1268.34087OpenAlexW2095803285MaRDI QIDQ354326

Fengjie Geng, Yan Cong Xu

Publication date: 18 July 2013

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-012-0563-3

zbMATH Keywords

pitchfork bifurcationgeneric heteroclinic looplocal coordinate moving framenonhyperbolic equilibrium

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Perturbations of ordinary differential equations (34D10) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (2)

Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system ⋮ Bifurcation of nongeneric homoclinic orbit accompanied by pitchfork bifurcation

Cites Work

• Unnamed Item
• Unnamed Item
• Bifurcations of multiple homoclinics in general dynamical systems
• Bifurcations of heterodimensional cycles with two saddle points
• Homoclinic bifurcation with nonhyperbolic equilibria
• Bifurcations of heterodimensional cycles with one orbit flip and one inclination flip
• Bifurcations of heteroclinic loops
• Local and global bifurcations with nonhyperbolic equilibria
• Bifurcations and chaotic dynamics in a 4-dimensional competitive Lotka-Volterra system
• A simplified optimal control method for homoclinic bifurcations
• Heteroclinic bifurcations near Hopf-zero bifurcation in reversible vector fields in \(\mathbb R^3\)
• Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit
• Codimension-one persistence beyond all orders of homoclinic orbits to singular saddle centres in reversible systems
• Bifurcation from codimension one relative homoclinic cycles
• BIFURCATIONS OF GENERIC HETEROCLINIC LOOP ACCOMPANIED BY TRANSCRITICAL BIFURCATION
• Theory and Application of a Nongeneric Heteroclinic Loop Bifurcation
• CODIMENSION 3 HETEROCLINIC BIFURCATIONS WITH ORBIT AND INCLINATION FLIPS IN REVERSIBLE SYSTEMS

This page was built for publication: Bifurcations of heteroclinic loop accompanied by pitchfork bifurcation