A codimension-two resonant bifurcation from a heteroclinic cycle with complex eigenvalues

Claire M. Postlethwaite, Jonathan H. P. Dawes
2006 Dynamical systems  
Robust heteroclinic cycles between equilibria lose stability either through local bifurcations of their equilibria or through global bifurcations. This paper considers a global loss of stability termed a 'resonant' bifurcation. This bifurcation is usually associated with the birth or death of a nearby periodic orbit, and generically occurs in either a supercritical or subcritical manner. For a specific robust heteroclinic cycle between equilibria with complex eigenvalues we examine the
more » ... ontwo point that separates the supercritical and subcritical. We investigate the bifurcation structure and show the existence of further bifurcations of periodic orbits.
doi:10.1080/14689360600552928 fatcat:y3zneaodh5asjla5kqxedft6rq