Evolution of the absolute magnetic flux (Φ, top panel) and of the injected magnetic flux (Φ_inj ≡ Φ−Φ(t = 0), bottom panel) in the system for the 7 parametric simulations. The non-eruptive simulation without surrounding field (No Erupt ND) is plotted with a continuous black line. The non-eruptive simulations with respectively (strong, medium, weak) arcade strength, labelled (No Erupt SD, No Erupt MD, No Erupt WD), are plotted respectively with a (purple dot dashed, blue dot-dot-dot-dashed, cyan dashed) line. The eruptive simulations with respectively (strong, medium, weak) arcade strength, labelled respectively (Erupt SD, Erupt MD, Erupt WD), are plotted respectively with a (red dashed, orange dot-dot-dot-dashed, yellow dot dashed) line.