Typical time evolution for the three planets in the 2:1-2:1 resonant chain after a close encounter with a flying-by star with mass 1 M_⊙ and inclination β = 45°. The distance of minimum approach between the two stars is q = 125 au. In the top panels from left to right, we show the period ratio between the adjacent pairs, the eccentricities and inclinations, while in the bottom panels, the two-body resonant angles for each pair (left and middle plots) and the three-body resonant angle (in the bottom right panel).