摘要
研究随机噪声对微生物连续培养的影响,引入白噪声描述营养消耗率受随机噪声的干扰,建立一类具有比率型功能反应函数的随机恒化器模型.通过构造Lyapunov函数,利用It公式证明系统正解的全局存在唯一性,并论证了系统的绝灭平衡点是全局随机渐近稳定的;探讨了噪声强度大小对随机模型的解围绕相应确定性模型的平衡点振荡行为的影响.通过数值模拟验证所得理论结果的正确性.
To explore the influence of random noise on microbial continuous culture, we establish a stochastic Chemostat model with ratio-dependent functional response in which white noise is introduced to describe nutrition conversion rate influenced by random noise. By constructing stochastic Lyapunov function and using the Itp formula, we prove that there is a unique positive solution in the system with positive initial value, and the washout equilibrium is stochastically asymptotic stable. Furthermore, we investigate the impact of white noise on the behavior of the solution spirals around the positive equilibrium of deterministic system. The numerical simulations support the proposed theoretical results.
出处
《深圳大学学报（理工版）》
EI
CAS
CSCD
北大核心
2016年第4期425-431,共7页
Journal of Shenzhen University(Science and Engineering)
基金
国家自然科学基金资助项目(11471007)
延安大学自然科学基金资助项目(YDKY201314)~~
关键词
随机微分方程
比率型功能反应函数
随机恒化器系统
随机渐近稳定
ITO公式
动力学行为
stochastic differential equation
ratio-dependent functional response
stochastic Chemostat
stochasti-cally asymptotic stable
It6 formula
dynamical behavior
