TY - JOUR
T1 - Periodic solutions of planar systems with two delays
AU - Ruan, Shigui
AU - Wei, Junjie
N1 - Funding Information:
The research of S.R. was supported by the Natural Science and Engineering Research Council of Canada and the Petro-Canada Young Innovator Award, and the research of J.W. was supported by the National Natural Science Foundations of China.
PY - 1999
Y1 - 1999
N2 - In this paper, we consider a planar system with two delays: ẋ1(t) = -a0x1(t) + a1F1(x1(t - τ1), x2(t - τ2)), ẋ2(t) = -b0x2(t) + b1F2(x1(t - τ1), x2(t - τ2)). 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.
AB - In this paper, we consider a planar system with two delays: ẋ1(t) = -a0x1(t) + a1F1(x1(t - τ1), x2(t - τ2)), ẋ2(t) = -b0x2(t) + b1F2(x1(t - τ1), x2(t - τ2)). 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.
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U2 - 10.1017/S0308210500031061
DO - 10.1017/S0308210500031061
M3 - Article
AN - SCOPUS:33746961598
VL - 129
SP - 1017
EP - 1032
JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics
JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics
SN - 0308-2105
IS - 5
ER -