BOUNDARY CRISES ARISING FROM SADDLE-NODE BIFURCATIONS IN PERIODICALLY FORCED MODELS

Abstract

An identical bifurcation sequence is identified for models of predator-prey interaction and glycolytic reaction under strong periodic forcing. It is determined that a symmetric saddle-node bifurcation gives rise to local chaotic attractors. These attractors are annihilated by a boundary crisis, but a stable periodic orbit persists. When this remaining periodic orbit subsequently loses stability, an intermittency transition to chaos is observed. Through the construction of return maps, the essential flow behavior is reduced to that of one-dimensional noninvertible maps. The equivalent scenario in these maps is determined to be a tangent bifurcation, followed by a boundary crisis and a subcritical period halving. A remarkable feature of this previously unrecognized bifurcation sequence is the existence of a chaotic set that changes from attracting to nonattracting and back to attracting.