Random dynamical systems

Random dynamical systems
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DOI:
10.1142/9789811228667_0013
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发表时间:
2020-12
期刊:
An Introduction to Nonautonomous Dynamical Systems and their Attractors
影响因子:
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通讯作者:
Zhisheng Shuai
Zhisheng Shuai
中科院分区:
其他
文献类型:
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作者:
Zhisheng Shuai

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如果R 0> 1,则(1 R 0,1 − 1 R 0)是全局稳定的;如果R 0 ≤ 1,则(1,0)是全局稳定的。注意,λ应该受到许多因素的影响。很难精确地确定。相反,我们经常让λ是一个随机变量,这更合适。然而,在随机λ下解的渐近行为是什么?例如,λ = λ1或λ2,其中R 0(λ1)> 1,R 0(λ2)≤ 1,并且P(λ = λ1)= P(λ = λ2)= 12。
If R0 > 1, ( 1 R0 , 1 − 1 R0 ) is globally stable; if R0 ≤ 1, then (1, 0) is globally stable. Note that λ should be affected by many factors. It’s difficult to be determined precisely. Instead, we often let λ is a random variable, which is more suitable. However, what’s the asymptotic behavior of solutions under random λ? For example, λ = λ1 or λ2, where R0(λ1) > 1, R0(λ2) ≤ 1, and P (λ = λ1) = P (λ = λ2) = 12 .