Periodic solutions of planar systems with two delays
Periodic solutions of planar systems with two delays
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DOI：
10.1017/s0308210500031061
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
S. Ruan;Junjie Wei
中科院分区：
文献类型：
--
作者：
S. Ruan;Junjie Wei
本文考虑一类具有两个时滞的平面系统：ẋ1(T)=−a0x1(T)+a1F1(x1(t−τ1)，x2(τ−T2))。ẋ2(T)=−b0x2(T)+b1F2(x1(t−τ1)，x2(t−τxs2))。首先，研究了系统的线性化稳定性和局部Hopf分支。然后，利用度论方法给出了非常数周期解存在的条件。最后，以一个简单的双时滞神经网络模型为例进行了分析。
In this paper, we consider a planar system with two delays: ẋ1(t) = −a0x1(t) + a1F1 (x1(t − τ1), x2(τ−t2)). ẋ2(t) = −b0x2(t) + b1F2 (x1(t − τ1), x2(t − τxs2)). Firstly, linearized stability and local Hopf bifurcations are studied. Then, existence conditions for non-constant periodic solutions are derived using degree theory methods. Finally, a simple neural network model with two delays is analysed as an example.