Crossover phenomenon in adversarial attacks on voter model

Abstract A recent study (Chiyomaru and Takemoto 2022 Phys. Rev. E 106 014301) considered adversarial attacks conducted to distort voter model dynamics in networks. This method intervenes the interaction patterns of individuals induces them be a target opinion state through small perturbation ε . In this study, we investigate on random networks finite size n The exit probability P +1 reach absorbing mean time τ consensus are analyzed mean-field approximation. Given > 0, converges asymptotically unity as increases. scales ( ln ϵ n stretchy="false">) / for homogeneous with large By contrast, it (\epsilon\mu_1^2n/\mu_2))/\epsilon$?> form="prefix">ln μ 1 2 heterogeneous , where µ 1 2 represent first second moments degree distribution, respectively. Moreover, observe crossover phenomenon from linear scale logarithmic find $n_{\mathrm{co}}\sim \epsilon^{-1/\alpha}$?> c mathvariant="normal">o ∼ − α above which all nodes becomes time. Here, α = $\alpha (\gamma-1)/2$?> = γ scale-free exponent $2\lt\gamma\lt3$?> < 3