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| 摘要: |
| 本文研究了带Poisson跳年龄相关随机时滞种群系统均方稳定性的问题.在一定条件下，给出了数值解均方稳定的定义.利用补偿随机θ法讨论系统数值解的均方稳定性，给出数值解稳定的充分条件.获得了当1/2 ≤ θ ≤ 1时，对于任意的步长△τ/m，数值解是均方稳定的；当0 ≤ θ < 1，时，如果步长△t∈（0，△t0），数值解是指数均方稳定的的结果.最后通过数值算例推广并验证了结果的有效性和正确性. |
| 关键词: 随机时滞种群系统 补偿随机θ法 Poisson跳 均方稳定 |
| DOI： |
| 分类号:O241.82 |
| 基金项目:宁夏大学科学研究基金资助项目（ZR16002）. |
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| MEAN-SQUARE STABILITY OF STOCHASTIC AGE-DEPENDENT DELAY POPULATION SYSTEMS WITH POISSON JUMPS |
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LI Qiang,KANG Ting,CHEN Fei-fei,ZHANG Qi-min
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| Abstract: |
| This paper deals with the mean-square stability problem of stochastic agedependent delay population systems with Poisson jumps. Under the certain conditions, the definition of mean-square stability of the numerical solution is given. By utilizing the compensated stochastic θ methods, the mean-square stability of the numerical solution is investigated and a sufficient condition for mean-square stability of the numerical solution is presented. It is shown that the compensated stochastic θ methods are mean-square stable for any stepsize △τ/m when 1/2 ≤ θ ≤ 1, and they are exponentially mean-square stable if the stepsize △t∈(0, △t0) when 0 ≤ θ < 1. Finally, the theoretical results are also confirmed by a numerical experiment. |
| Key words: stochastic age-dependent delay population systems compensated stochastic θ method Poisson jumps mean-square stability |
