Probability of positive consensus <i>P</i>₊ in a system of two interconnected networks <i>A</i> and <i>B</i>.

<p>Initially, all nodes in network <i>A</i> (<i>B</i>) are positive (negative). (a) <i>P</i>₊ as function of <i>r</i> = <i>p</i>/<i>q</i> on a log-linear scale, for networks of size <i>N</i> = 2048 nodes and <i>β</i> = 2.0 (∘), 2.25 (□) and 2.5 (◇). At the crossover point <i>r</i>*(<i>β</i>) is <i>P</i>₊ = 1/2 (vertical dashed line shown for <i>β</i> = 2.5 only). (b) <i>P</i>₊ vs <i>β</i> for <i>r</i> = 0.25 (∘), 1.0 (□) and 1.2 (◇). At <i>β</i>*(<i>r</i>) is <i>P</i>₊ = 1/2 (vertical dashed line for <i>r</i> = 0.25). Inset: mean consensus time <i>τ</i> vs <i>β</i>, for the same parameter values, showing a maximum at <i>β</i>*. (c) <i>P</i>₊ vs <i>β</i> for <i>r</i> = 0.25 and network sizes <i>N</i> = 512 (∘), 2048 (□), 8192 (◇) and 32768 (△). Inset: the curves collapse when the <i>x</i>-axis is rescaled by . All numerical results correspond to an average over 10⁴ independent realizations on degree-regular random networks of degree <i>μ</i> = 5.