Threshold to global diffusion in a nonmonotonic map with quadratic nonlinearity

In this paper the threshold to global diffusion of a nonmonotonic map, with quadratic nonlinearity, using a forcing function K sin theta as in the sta ndard map. is analyzed. For low values of the stochastic parameter K the br eaking of the last KAM curve is caused by the period-one reconnecting reson ance. At higher K secondary resonances play an increasingly important role. Two kinds of KAM curves are studied: those between reconnecting resonances and those outside a reconnecting resonance pair. Using a perturbative Hami ltonian method to determine the resonance width a weak overlap criterion is used to estimate the breaking of the last KAM curve outside of the reconne cting islands. For some values of the parameters a nonintegrable reconnecti ng threshold is found above the threshold of global diffusion. In this regi me the reconnection increases the diffusion coefficient to a value close to the quasilinear value of the standard map. (C) 1999 Elsevier Science B.V. All rights reserved.