  Research on social contagion dynamics has not yet including a theoretical
analysis of the ubiquitous local trend imitation (LTI) characteristic. We
propose a social contagion model with a tent-like adoption probability
distribution to investigate the effect of this LTI characteristic on behavior
spreading. We also propose a generalized edge-based compartmental theory to
describe the proposed model. Through extensive numerical simulations and
theoretical analyses, we find a crossover in the phase transition: when the LTI
capacity is strong, the growth of the final behavior adoption size exhibits a
second-order phase transition. When the LTI capacity is weak, we see a
first-order phase transition. For a given behavioral information transmission
probability, there is an optimal LTI capacity that maximizes the final behavior
adoption size. Finally we find that the above phenomena are not qualitatively
affected by the heterogeneous degree distribution. Our suggested theory agrees
with the simulation results.
