基于微分方程的随机网络舆论传播模型研究与分析

Research and Analysis of Stochastic Network Public Opinion Propagation Model Based on Differential Equation

考虑到舆论传播模型往往受到环境噪音的影响,本文提出了媒体影响下的网络虚假舆论传播模型非线性动力学模型。首先,考虑到舆论传播过程中存在随机的不确定因素,将随机白噪声引入非线性动力学传播模型,从而使模型更加真实反应现实情况;其次,基于微分方程稳定性理论,对模型进行了数学分析,从而以理论推断舆论传播方式以及系统在平衡点最终状态;最后,在MATLAB中对所提模型进行数值模拟。结果表明,模型数值模拟情况与理论推导中正不变集分析和正解存在唯一性分析结果一致。数值模拟结果验证了所提模型的有效性。

Considering that the public opinion propagation model is often affected by environmental noise,this paper proposes a nonlinear dynamic model of network false public opinion propagation under model the influence of media.At the same time,considering the random uncertain factors in the process of public opinion propagation,the random white noise was introduced into the nonlinear dynamic propagation model,so that the model could more truly reflect the real situation.Further,based on the stability theory of differential equations,the mathematical analysis of the model was carried out to infer the mode of public opinion propagation and the final state of the system at the equilibrium point.Finally,the proposed model was numerically simulated in MATLAB.The results show that the numerical simulation of the model is consistent with the results of positive invariant set analysis and positive solution existence and uniqueness analysis in theoretical derivation.Numerical simulation results further verifying the effectiveness of the proposed model.