Time evolution of the resonant angle σ for the L4 (panel a) and L5 (panel b) test Trojans starting symmetric tadpole orbits, given initial σ = 90° and σ = 270° (i.e. σ = −90°), respectively. In the case of a non-migrating Jupiter, the σ evolution of these two objects are nicely symmetric, as indicated by the black curves. In the case of an outward migrating Jupiter with the speed of AU yr⁻¹ (> ), as indicated by the green curves, both Trojans have their resonant amplitudes increased but the L4 one’s resonant amplitude is less excited.