随机单种群Gompertz增长模型的稳定性

Stability for a Stochastic Single Species Gompertz Growth Model

研究一个随机单种群Gompertz增长模型,证明方程的每个从正初始值出发的解都是一个全局正解,得到这个解及其均值的解析表达式。引入随机变量依均值吸引和依均方吸引的概念,研究随机Gompertz方程,证明随机Gompertz方程的解是依均值吸引和依均值平方全局吸引,并存在唯一依均值的平方全局稳定的随机解。最后,证明随机Gompertz方程的解是最终随机有界的。

A stochastic single species Gompertz growth model was considered.It was shown that the equation had a global positive solution starting from the positive initial value and obtain its explicit expression.The expectation of the solution was also obtained.It was obtained that the equation was globally attractive in the mean square,and it was shown that there existed a unique solution of the model which was globally stable in the mean square.Finally,it was established that the solution of the equation was stochastically ultimately bounded.