Optimal imitation capacity and crossover phenomenon in the dynamics of social contagions

In the threshold model of social contagions with non-redundant memory, researchers have overlooked the investigation on the limited imitation (LI) effect, which shows individual imitates the behavior adoption only for a certain range of ratio of his adopted informants. To understand such LI effect, we propose a social contagion model with a gate-like adoption probability consisting of the 'on' and 'off' thresholds. With extensive numerical simulations, we find that, given information transmission probability and a gate width (the 'off' threshold minus the 'on' threshold), there exists an optimal imitation capacity with the optimal 'on' threshold maximizing the final adoption size. And the large 'off' threshold serves for further enlarging the final adoption size at a given 'on' threshold. Besides, a cross phenomenon in phase transition is also uncovered: the increase of 'on' threshold causes the growth pattern of final behavior adoption size versus the information transmission probability change from the second-order to the first-order phase transition. We finally find that the above phenomena are qualitatively unaffected by the heterogeneity level of degree distribution. At last, an edge-based compartmental theory is conceived for theoretical analysis. And our suggested theory agrees well with the simulation results.

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