On the Bautin bifurcation for systems of delay differential equations
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چکیده
The existence of periodic solutions for evolution equations is of certain interest for both pure and applied mathematicians. Even for bidimensional systems of differential equations the detection of limit cycles by theoretical means is difficult. The bifurcation theory offers a strong tool for finding limit cycles, namely the theory concerning the Hopf bifurcation (when there is a varying parameter)[2], [6]. Several authors studied the Hopf bifurcation for delay differential equations (e.g. [4], [7], [1], [5] ). We are interested to find sufficient conditions for the Bautin bifurcation for a class of such systems.
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