摘要
为探究环境噪声对谣言传播的影响,建立了一类具有随机扰动的谣言传播模型.首先,利用Ito公式验证了模型正解的全局存在唯一性;其次,通过构造Lyapunov函数证明了当R0 〈1时,传谣者和免疫者将依指数趋于灭绝;当R0 〉1且σ^2 〈2（β -γ -b） 时,系统是随机强平均持久的;再次,证明了当噪声强度较小时随机模型的解将围绕相应确定性模型的正平衡点振荡,且振幅与噪声强度有关;最后,通过数值模拟验证了所得理论结果的正确性.
Considering the influence of the noise in the environment, we construct a stochastic rumortransmission model. By using the Ito formula, we first obtain the global existence and uniqueness of thepositive solution. Then we show the spreaders and stiflers will tend to zero exponentially almost surelyunder the condition R0 〈1 ; when R0 〉1 and σ2 〈2（β -γ -b） , the stochastic system is strong persistentin mean. Furthermore, we show that the solution of the stochastic model spirals around the correspondingequilibrium of the deterministic model when the noise intensity is small, and the intensity of fluctuationis proportional to that of the white noise. Finally, these results are illustrated by computer simulations.
出处
《科技通报》
北大核心
2016年第6期139-144,199,共7页
Bulletin of Science and Technology
关键词
谣言传播
ITO公式
动力学行为
灭绝
持久性
rumor spreading
Ito formula
dynamics behavior
extinction
persistence
