Noisy parametric sweep through a period-doubling bifurcation of the Hénon map

Previous results on linear parametric sweep through period-doubling bifurcations of a one-dimensional map are extended to the two-dimensional case. An explicit noise model is also included. Matched asymptotic expansions together with a centre-manifold reduction in the vicinity of the bifurcation are used to describe trajectories sweeping up or down. The role of noise in triggering the transition from period-1 to period-2 is emphasised. Increasing sweep rate delays the transition; increasing noise level reduces the delay.