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Dynamic of a stochastic predator-prey population. (English) Zbl 1238.92055
Summary: A stochastic predator-prey model is studied. First we prove the existence, uniqueness and positivity of solutions. Then we show the upper bounds for the moments and the growth rate of the population. In some cases, the growth rate is negative and the population dies out rapidly. The paper ends with some reviews of the paper of B.G. Zhang and K. Gopalsamy, Stochastic Anal. Appl. 18, No. 2, 323–331 (2000; Zbl 0983.92023).
MSC:
92D40Ecology
60H10Stochastic ordinary differential equations
34F05ODE with randomness
References:
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[13]Zhang, B. G.; Gopalsamy, K.: On the periodic solution of N-dimentional stochastic population models, Stoch. anal. Appl. 18, No. 2, 323-331 (2000) · Zbl 0983.92023 · doi:10.1080/07362990008809671