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Periodic solutions of planar systems with two delays

  • Shigui Ruan (a1) and Junjie Wei (a2)


In this paper, we consider a planar system with two delays:

1(t) = −a0x1(t) + a1F1 (x1(tτ1), x2(τt2)).

2(t) = −b0x2(t) + b1F2 (x1(tτ1), x2(tτxs2)).

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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