Bifurcations of periodic solutions of delay differential equations.

*(English)*Zbl 1027.34081The author extends the method of J. L. Kaplan and J. A. Yorke [J. Differ. Equations 23, 293-314 (1977; Zbl 0307.34070)] to prove the existence of periodic solutions with certain period in scalar delay differential equations of the type \(\dot x(t)= F(x(t), x(t-r), x(t-2r))\), where \(F\) satisfies the relation \(F(x,y,-x)=-F(-x,-y,x)\). For \(F\) depending on parameters, the paper gives conditions under which Hopf and saddle-node bifurcations of periodic solutions occur. Moreover, the author provides examples showing that Hopf and saddle-node bifurcations often occur infinitely many times.

Reviewer: Jan Sieber (Bristol)

##### MSC:

34K18 | Bifurcation theory of functional-differential equations |

34K13 | Periodic solutions to functional-differential equations |

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\textit{M. Han}, J. Differ. Equations 189, No. 2, 396--411 (2003; Zbl 1027.34081)

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##### References:

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