中文摘要：

社交网络是当前最重要的信息传播媒体之一。近年来,由谣言传播引发的事件时有发生,因此有必要研究社交网络中谣言的传播规律。根据Ebbinghaus遗忘规律,研究遗忘机制对谣言传播的影响规律,建立了以遗忘率为指数函数形式的谣言传播模型。通过对4种人群建立平均场方程,计算了基本再生数,对模型的传播规律进行了理论分析。通过在社交网络中实验,研究网络中4种人群的变化规律,分析遗忘率函数的各参数对谣言传播的影响,并且将遗忘率为指数函数和常数形式做了对比。实验结果表明：遗忘率对传播者和免疫者的密度影响显著,初始遗忘概率越大,或者遗忘速度越快,谣言的传播力越弱;相对于遗忘率为常数的情形,遗忘率为指数函数形式时更符合谣言传播的实际情况。仿真实验验证了理论分析的正确性,并据此提出了谣言控制策略。此项研究有助于深入理解谣言的传播行为,可为网络舆论的传播过程及预测提供参考。

英文摘要：

Social networking is the most important medium for information spreading but incidents occur recently because of rumor spreading; so it is necessary to study how to reduce rumor spreading in social networking to a minimum. A rumor spreading model with forgetting mechanism considered is proposed in order to solve the problem of rumor spreading in social networking. In accordance with the forgetting rule of Ebbinghaus,we establish the model of exponential functional forgetting rate. The mean field equations of the model are established to describe the susceptible,the infected,know but not the infected,and the removed. The basic reproductive number is calculated and the spreading rules of the model are analyzed theoretically. We study the rules of four groups of throngs and analyze the influence of various parameters of forgetting function on rumor spreading. We compare the rumor spreading of exponential function forgetting rate and constant forgetting rate. The experiment results show that,the exponential forgetting rate can reflect the actual situation better： the forgetting rate has significant effect on the density of infected and removed,the greater the initial forgetting rate or forgetting speed,the weaker is the rumor spreading; compared with the case of constant forgetting rate,the exponential function forgetting rate is more in line with the actual situation of rumor spreading. The correctness of theoretical analysis is verified by simulation experiments and the control strategy of rumor is also proposed. The research results are helpful to understanding the behavior of rumor spreading and provide useful reference for the spreading process and the prediction of network public opinion.