Lévy噪声和高斯白噪声共同激励的肿瘤细胞生长模型的平均首次穿越时间  

Mean first passage time of tumor growth model under excitation of Lévy noise and Gaussian white noise

作　　者：樊顺厚[1] 姚婷 郭永峰 王琳杰 FAN Shun-hou;YAO Ting;GUO Yong-feng;WANG Lin-jie(School of Mathematical Sciences,Tiangong University,Tianjin 300387,China))

机构地区：[1]天津工业大学数学科学学院,天津300387

出　　处：《天津工业大学学报》2020年第2期76-82,共7页Journal of Tiangong University

基　　金：国家自然科学基金资助项目(11672207,11501410);天津市自然科学基金资助项目(17JCYBJC15700)。

摘　　要：为研究肿瘤细胞消亡和复发的转换时间,探讨了由Lévy噪声和高斯白噪声共同激励下肿瘤细胞生长模型的平均首次穿越时间(MFPT)问题。根据平均首次穿越时间的定义,利用四阶Runge-Kutta法和JanickWeron算法,分别将其作为Lévy噪声强度D和高斯白噪声强度Q的函数进行研究,计算系统的平均首次穿越时间,并探讨Lévy噪声和高斯白噪声对肿瘤细胞生长的影响。结果表明:随着Lévy噪声强度D的增加,粒子由健康状态到患病状态的平均首次穿越时间T+(x1→x3)逐渐减小,而T-(x3→x1)逐渐增大,说明虽然Lévy噪声强度对系统实现两个状态间跃迁的影响有所不同,但这都不利于肿瘤细胞的消亡;当肿瘤细胞的数量处于高水平时,增加高斯白噪声的强度Q对肿瘤细胞的减少有积极作用;稳定性指标α和偏斜参数β在肿瘤生长动力学中以相反的方式起作用。In order to study the transition time of extinction and recurrence of tumor cell,the mean first passage time of a tumor growth model under the excitation of Lévy noise and Gaussian white noise is investigated.According to the definition of the mean first passage time,the fourth-order Runge-Kutta method and Janick-Weron algorithm are used to study the mean first passage time as a function of Lévy noise intensity D and Gaussian white noise intensity Q respectively.The mean first passage time of the system is calculated and the influences of Lévy noise and Gaussian white noise on tumor cell growth are discussed.The results indicate that:As the Lévy noise intensity D increases,the mean first passage time of particles from a healthy state to a diseased state T+(x1→x3)gradually decreases,and T-(x3→x1)increases,which indicates that although the Lévy noise intensity has different effects on the transition between the two states,it is not conducive to the extinction of tumor cells.When the number of tumor cells is at a high level,increasing the Gaussian white noise intensity has a positive effect on the reduction of tumor cells.Stability indexαand skewness parameterβwork in the opposite way in tumor growth dynamics.

关 键 词：Lévy噪声 高斯白噪声 Logistic系统 肿瘤细胞生长模型 平均首次穿越时间 

分 类 号：O414.2[理学—理论物理] O415.6[理学—物理]