Dependence of the real part ω of the eigenfrequencies and the corresponding damping rate γ/ω in the two-loop system as a function of the density in the right tube ζ_R for fixed ζ_L = 3 and d/R = 3. a) Eigenfrequencies ω₊ (thick dashed line) and ω₋ (full line) as a function of ζ_R, together with the Alfvén frequencies of the left and right tubes (dashed-dotted lines), marking two transition points between standard and anomalous systems (indicated by saR and saL on the horizontal axis, referring to the loop that cannot support the global oscillation), and the individual kink frequencies of the two tubes (dotted and dashed lines). b) Ratio of damping rate to real part of the eigenfrequency of the two-loop system γ/ω₀, where ω₀ can be either ω₊ (thick dashed line) or ω₋ (full line), and of the left (dotted line) and right (dashed line) loop as a function of ζ_R.