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Zbl 1027.34081
Han, Maoan
Bifurcations of periodic solutions of delay differential equations.
(English)
[J] J. Differ. Equations 189, No.2, 396-411 (2003). ISSN 0022-0396

The author extends the method of {\it J. L. Kaplan} and {\it 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.
[Jan Sieber (Bristol)]
MSC 2000:
*34K18 Bifurcation theory of functional differential equations
34K13 Periodic solutions of functional differential equations

Keywords: delay differential equation; periodic solution; bifurcation

Citations: Zbl 0307.34070

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