Periodic solutions of planar systems with two delays

In this paper, we consider a planar system with two delays: (x) over dot(1)(t) = -a(0)s(1)(t) + a(1)F(1)(x(1)(t - tau(1)), x(2)(t - tau (2))), (x) over dot(2)(t) = -b(0)x(2)(t) + b(1)F(2)(x(1)(t - tau(1)), x(2)(t - tau (2))). Firstly, linearized stability and local Hopf bifurcations are studied. Then , existence conditions for non-constant periodic solutions are derived usin g degree theory methods. Finally, a simple neural network model. with two d elays is analysed as an example.