馬 超, 黎定仕

(西南交通大學(xué)數(shù)學(xué)學(xué)院,四川成都610031)

1 預(yù)備知識

微分積分方程穩(wěn)定性的問題具有其特定的物理意義,許多學(xué)者對其進(jìn)行了深入的探究[1-6].微分積分方程在多個科學(xué)領(lǐng)域中,如控制理論、生物、經(jīng)濟(jì)、醫(yī)學(xué)等都會遇見,考慮其后效反應(yīng)或者時滯狀態(tài)[7-8]已經(jīng)成為了必要.特別地,人們常常用微分積分方程來描述具有遺傳性質(zhì)的模型.而在這些領(lǐng)域中常見的時滯現(xiàn)象包括常數(shù)時滯和變量時滯[9-14],但是由于存在大量軸突大小和長度類似的路徑,微分積分方程常常會有空間上的外延性.于是,會有沿著這些路徑的傳導(dǎo)速度和傳播時滯的不同的現(xiàn)象產(chǎn)生.在這種情況下,信號的傳播不再是瞬間的,也不能用離散時滯來模擬,從而就出現(xiàn)了一種更為合適的描述,即連續(xù)的分布式時滯.

本文研究如下非自治微分積分方程

2 主要結(jié)果

3 例子

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