具有饱和控制的时滞反应扩散谣言传播模型

Time-Delay Reaction-Diffusion Rumor Propagation Model with Saturation Control

Hopf分岔是一种比较简单而又重要的动态分岔问题,是指系统参数变化经过临界值时,平衡点由稳定变为不稳定并产生极限环.基于Hopf分岔,文章提出了一个具有饱和控制的时滞反应扩散谣言传播模型,其更好地反映了现实生活中谣言传播的特性,并且研究了其Turing不稳定和Hopf分岔,同时选择时滞为分岔参数,给出了分岔阈值的解析表达.最后,通过数值模拟仿真验证了理论结果的正确性,其结果表明扩散和时滞均是导致系统不稳定的原因.传统的谣言传播模型只考虑了时间演化,而该模型从时间和空间两个维度刻画了传统的谣言传播模型,使其更加贴切地反映了谣言在现实生活中的传播规律,为谣言传播的治理提供新的思路.

Hopf bifurcation is a kind of simple but important dynamic bifurcation problem,which means that when the system parameter changes past the critical value,the equilibrium point changes from stable to unstable and a limit cycle is generated.Based on Hopf bifurcation,this paper proposes a time-delay reaction-diffusion rumor propagation model with saturated control,which better reflects the characteristics of rumor propagation in real life,and studies the Turing instability and Hopf bifurcation.Meanwhile,the time delay is selected as the bifurcation parameter,and the analytic expression of the bifurcation threshold is given.Finally,the correctness of the theoretical results is verified by numerical simulation.The results show that both diffusion and time delay are the causes of the system instability.The traditional rumor propagation model only considers the time evolution,while the model depicts the traditional rumor propagation model from the two dimensions of time and space,making it more appropriate to reflect the law of rumor propagation in real life,and providing new ideas for the governance of rumor propagation.