The dynamics of the blackmail propagation model based on small-world networks is investigated. It is found that for a given transmitting probability λ the dynamical behavior of blackmail propagation transits from linear growth type to logistical growth one with the network randomness p increases. The transition takes place at the critical network randomness pc=1/N, where N is the total number of nodes in the network. For a given network randomness p the dynamical behavior of blackmail propagation transits from exponential decrease type to logistical growth one with the transmitting probability λ increases. The transition occurs at the critical transmitting probability λc=1/〈k〉, where 〈k〉 is the average number of the nearest neighbors. The present work will be useful for understanding computer virus epidemics and other spreading phenomena on communication and social networks.

中文翻译：

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小世界网络上的勒索传播

研究了基于小世界网络的勒索传播模型的动力学。研究发现，对于给定的传输概率 λ，勒索传播的动态行为随着网络随机性 p 的增加从线性增长型转变为逻辑增长型。转换发生在临界网络随机性 pc=1/N，其中 N 是网络中的节点总数。对于给定的网络随机性 p，勒索传播的动态行为从指数下降型转变为逻辑增长型，传输概率 λ 增加。转换发生在临界传输概率 λc=1/<k> 处，其中 <k> 是最近邻居的平均数。