caa a22 4500 388108843 CHVBK 20180307125347.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500031061 doi S0308210500031061 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500031061 Periodic solutions of planar systems with two delays [Elektronische Daten] 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. Copyright © Royal Society of Edinburgh 1999 Ruan Shigui Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5 Wei Junjie Department of Mathematics, Northeast Normal University, Changchun, Jilin 130024, People's, Republic of China Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/5(1999), 1017-1032 0308-2105 129:5<1017 1999 129 PRM https://doi.org/10.1017/S0308210500031061 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500031061 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ruan Shigui Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5 NATIONALLICENCE 700 1- Wei Junjie Department of Mathematics, Northeast Normal University, Changchun, Jilin 130024, People's, Republic of China NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/5(1999), 1017-1032 0308-2105 129:5<1017 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge