LAUSR

Abstract We consider a single degree freedom oscillator in order to accurately represent some modelling with ship roll damping. The proposed oscillator is a nonsmooth Rayleigh-Duffing equation x + a x + b x | x | + c x + d x 3 = 0 . The main goal of this paper is to study the global dynamics of the nonsmooth Rayleigh-Duffing oscillator in the case d 0 , i.e., the saddle case. The nonsmooth Rayleigh-Duffing oscillator is only C 1 so that many classical theory cannot be applied directly. In order to see the tendency of evolutions in a large range, we study not only its finite equilibria but also the equilibria at infinity. We find necessary and sufficient conditions for existence of limit cycles and heteroclinic loops respectively. Finally, we give the complete global bifurcation diagram and classify all global phase portraits in the Poincare disc in global parameters.