Paths of semi-major axis versus eccentricity, and semi-major axis versus inclination for a representative set of three different HR 8799 systems. Panel (a): Isolated resonant HR 8799 system. All four planets remain planar and oscillate around their initial semi-major axis and eccentricity. No other changes occur. Panel (b): Perturbed resonant HR 8799 system dissolving before the cutoff time. Only HR 8799 b’s semi-major axis attains some stability after a strong perturbation, before a planet is lost. Panel (c): Perturbed non-resonant HR 8799 system surviving to cutoff, despite dissolving in isolation (see Sect. 3.2.1). Two planets move inwards and two planets move outwards. All planets, except for HR 8799 c (green), remain at their new semi-major axes. The orientations of the orbits are not fixed.