摘要
研究了含时滞项的非对称双稳系统中的平均首次穿越时间问题.应用小时滞近似方法,得到了系统的Fokker-Planck方程及稳态概率密度函数,进而得到了系统的平均首次穿越时间的表达式,最后对理论结果做了数值模拟.数值计算结果表明:(1)时滞量的大小对系统的稳态概率密度函数的影响是不一样的,当0<τ<0.175时,系统的稳态概率密度函数曲线仍然为双峰形状;当τ>0.175时,系统的稳态概率密度函数曲线呈现出阱状.(2)在0<τ<0.175时,讨论了系统的乘性和加性噪声强度对系统的平均首次穿越时间的影响,发现平均首次穿越时间T+-乘性噪声强度曲线上有最小值出现,而T+-加性噪声强度曲线是单调的.
The mean first-passage time in an asymmetric bistable system with time-delayed feedback was investigated. Under the condition of small time delay approximation theory, the approximate Fokker-Planck equation and the stationary probability distribution function were obtained, then the expression of the mean first-passage time was obtained, and the theoretical results by numerical simulation were discussed . Numerical results show that ： （ 1 ） The value of the delay time can cause different effects on the stationary probability distribution function： when, there are still two peaks in the curve of the stationary probability distribution; when, there exists a valley in the curve of the stationary probability distribution; （2） when, we studied the effects of multiplicative noise intensityand curve of - , while ad the ditive noise intensity on the mean first-passage time, and found there existed a valley in the curve of - a was monotonic
出处
《动力学与控制学报》
2007年第4期298-301,共4页
Journal of Dynamics and Control
基金
国家自然科学基金(10472091
10332030)资助项目~~
关键词
时滞反馈
稳态概率分布
非对称双稳系统
平均首次穿越时间
time-delayed feedback, stationary probability distribution, asymmetric bistable system, meanfirst-passage time
