一类高阶非线性随机时滞微分方程的一般衰减速率分析

Analysis of General Decay Rates for a Class of Highly Nonlinear Stochastic Delay Differential Equations

分别讨论了高阶非线性常时滞和中立型随机微分方程以一般衰减速率渐近稳定所需满足的条件。在系数满足局部Lipschitz条件和基于Lyapunov函数的Khasminskii型条件下,证明了方程存在唯一解并且依一般衰减速率稳定。通过算例验证了所得结论的有效性。

The conditions for asymptotic stability of high order nonlinear stochastic differential equations with constant delay and neutral type at general decay rate are discussed,respectively.It is proved that under the conditions of local Lipschitz condition and Khasminskii-type conditions based on Lyapunov functions,the equations will have unique solutions and be stable with general decay rates.The validity of results was checked by illustrative examples.