TY - JOUR
T1 - Homoclinic saddle to saddle-focus transitions in 4D systems
AU - Kalia, Manu
AU - Kouznetsov, Iouri Aleksandrovitsj
AU - Meijer, Hil Gaétan Ellart
PY - 2019/6
Y1 - 2019/6
N2 - A saddle to saddle-focus homoclinic transition when the stable leading eigenspace is three-dimensional (called the 3DL bifurcation) is analyzed. Here a pair of complex eigenvalues and a real eigenvalue exchange their position relative to the imaginary axis, giving rise to a 3D stable leading eigenspace at the critical parameter values. This transition is different from the standard Belyakov bifurcation, where a double real eigenvalue splits either into a pair of complex-conjugate eigenvalues or two distinct real eigenvalues. In the wild case, we obtain sets of codimension 1 and 2 bifurcation curves and points that asymptotically approach the 3DL bifurcation point and have a structure that differs from that of the standard Belyakov case. We give an example of this bifurcation in a perturbed Lorenz–Stenflo 4D ordinary differential equation model.
AB - A saddle to saddle-focus homoclinic transition when the stable leading eigenspace is three-dimensional (called the 3DL bifurcation) is analyzed. Here a pair of complex eigenvalues and a real eigenvalue exchange their position relative to the imaginary axis, giving rise to a 3D stable leading eigenspace at the critical parameter values. This transition is different from the standard Belyakov bifurcation, where a double real eigenvalue splits either into a pair of complex-conjugate eigenvalues or two distinct real eigenvalues. In the wild case, we obtain sets of codimension 1 and 2 bifurcation curves and points that asymptotically approach the 3DL bifurcation point and have a structure that differs from that of the standard Belyakov case. We give an example of this bifurcation in a perturbed Lorenz–Stenflo 4D ordinary differential equation model.
KW - Homoclinic bifurcations
KW - Numerical bifurcation analysis
UR - http://www.scopus.com/inward/record.url?scp=85069474696&partnerID=8YFLogxK
U2 - 10.1088/1361-6544/ab0041
DO - 10.1088/1361-6544/ab0041
M3 - Article
SN - 0951-7715
VL - 32
SP - 2024
EP - 2054
JO - Nonlinearity
JF - Nonlinearity
IS - 6
ER -