Exponential stability of stochastic age-dependent population dynamics system
一类随机人口发展系统的指数稳定性

The influence of the stochastic external environment upon the population dynamics system have never been considered in ordinary age-dependent system models.A class of stochastic age-dependent population dynamics system is proposed,on the condition that migration is perturbed by random external environment.The mean square and almost sure exponential stability of stochastic age-dependent population dynamics system are discussed in Hilbert space.Sufficient conditions of mean square and almost sure exponential stability are established for a class of stochastic age-dependent population dynamics system.The analyses are conducted by using Burkholder-Davis-Gundy inequality,Gronwall lemma and Kolmogorov inequality derived for our stability purposes.It is also proposed that if the birth rate can be regarded as a controllable variable,the system is still mean square and almost sure exponential stability.The optimal control can be further studied for stochastic age-dependent population dynamics system.