STOCHASTIC DELAY POPULATION DYNAMICS
STOCHASTIC DELAY POPULATION DYNAMICS
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发表时间：
2004
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通讯作者：
A. Bahar;X. Mao
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作者：
A. Bahar;X. Mao
本文对时滞Lotka-Volterra模型ux（t）= diag（x_1（t）; x_n（t））进行随机扰动（B + Ax（t）+ Bx（t-ε））转化为随机时滞微分方程dx（t）= diag（x1（t）; ε; xn（t））（（B + Ax（t）+ Bx（t-Δ））dt+ Δ dw（t）），并证明在一定条件下，原始延迟等于-的作用和相关的随机延迟方程的行为类似的意义下，都有正解，不会爆炸到无穷大，时间是有限的，事实上，最终是有界的。换句话说，我们表明，在一定条件下，噪声不会破坏这些良好的性质。然而，我们也将证明，在某些其他条件下，虽然原来的延迟方程的解可能是持久的，相关的随机延迟方程的解将成为灭绝的概率为1。这揭示了环境噪声可能导致种群灭绝的重要事实。
In this paper we stochastically perturb the delay Lotka-Volterra model u x(t) = diag(x1(t); � � � ; xn(t))(b + Ax(t) + Bx(t − � )) into the stochastic delay differential equation dx(t) = diag(x1(t); � � � ; xn(t)) ((b + Ax(t) + Bx(t − � ))dt+�dw (t)), and show that under certain conditions,the original delay equa- tion and the associated stochastic delay equation behave similarly in the sense that both have positive solutions which will not explode to infinity in a finite time and, in fact, will be ultimately bounded. In other words, we show that un- der certain condition the noise will not spoil these nice properties. However, we will also show, under some other conditions, that although the solution to the original delay equation may be persistent, the solution to the associated stochas- tic delay equation will become extinct with probability one. This reveals the important fact that the environmental noise may make the population extinct.