Construction of codimension one homoclinic cycles

Authors :: Jürgen Knobloch
Ale Jan Homburg
Maria Kellner
Analysis (KDV, FNWI)
Mathematics
Source :: Dynamical Systems, 29(1), 133-151. Taylor and Francis Ltd., Homburg, A J, Kellner, M & Knobloch, J 2014, ' Construction of codimension one homoclinic cycles ', Dynamical Systems-an International Journal, vol. 29, no. 1, pp. 133-151 . https://doi.org/10.1080/14689367.2013.860085, Dynamical Systems-an International Journal, 29(1), 133-151. Taylor and Francis Ltd.
Publication Year :: 2013
Publisher :: Informa UK Limited, 2013.
Abstract: We give an explicit construction of families of Dm-equivariant polynomial vector fields in possessing a codimension one homoclinic cycle. The homoclinic cycle consists of m homoclinic trajectories all connected to the equilibrium at the origin. The constructed vector fields can provide a setting for a (numerical) bifurcation study of these homoclinic cycles, in particular for m equal to a multiple of 4, where the bifurcations form an open problem. © 2013 © 2013 Taylor & Francis.