Stability of the delay logistic equation of population dynamics

2003 IEEE International Workshop on Workload Characterization (IEEE Cat. No.03EX775) Pub Date : 2003-08-20 DOI:10.1109/PHYCON.2003.1236839

M. Vagina

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引用次数: 1

Abstract

The nonlinear logistic equation dy/dt=/spl epsiv/y(t) (1-/spl Sigma//sub k=0/ /sup n/b/sub k/y(t-/spl tau//sub k/), /spl epsiv/>0, b/sub k/, /spl tau//spl isin/(0;/spl infin/) (0/spl les/k/spl les/n) is discussed. The local stability of the nonzero stationary solution of this equation depends on the stability of linear equation dx/dt=-/spl Sigma//sub k=1/ /sup n/ a/sub k/x(t-/spl tau//sub k/), where a/sub k/=/spl epsiv/b/sub k///spl Sigma//sub j=0/ /sup n/b/sub j/ (0/spl les/k/spl les/n). It is shown that the condition /spl Sigma//sub k=1/ /sup n/a/sub k//spl tau//sub k/0, k=0,l, ..., n), then the stationary solution y/spl equiv/1//spl Sigma//sub k=0/ /sup n/b/sub k/ of logistic equation is stable with respect to small perturbations when the sequence (b/sub k/) is nonnegative and convex.

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种群动力学时滞logistic方程的稳定性

讨论了非线性logistic方程dy/dt=/spl epsiv/y(t) (1-/spl Sigma//sub k=0/ /sup n/b/sub k/y(t-/spl tau//sub k/)， /spl epsiv/>， b/sub k/， /spl tau//spl isin/(0;/spl infin/) (0/spl les/k/spl les/n)。该方程非零平稳解的局部稳定性取决于线性方程dx/dt=-/spl Sigma//下标k=1/ /sup n/ a/下标k/x(t-/spl tau//下标k/)的稳定性，其中a/下标k/=/spl epsiv/b/下标k///spl Sigma//下标j=0/ /sup n/b/下标j/ (0/spl les/k/spl les/n)。结果表明:/spl σ //下标k=1/ /sup n/a/下标k//spl τ //下标k/0, k= 0,1，…， n)，则logistic方程的平稳解y/spl equiv/1//spl Sigma//下标k=0/ /sup n/b/下标k/当序列(b/下标k/)为非负凸时，对于小扰动是稳定的。

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2003 IEEE International Workshop on Workload Characterization (IEEE Cat. No.03EX775)

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