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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