Bifurcation of Periodic Delay Differential Equations at Points of 1:4 Resonance

Röst, Gergely (2006) Bifurcation of Periodic Delay Differential Equations at Points of 1:4 Resonance. Functional Differential Equations, 13 (3-4). pp. 585-602. ISSN 0793-1786

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Abstract

The time-periodic scalar delay differential equation \dot{x}(t) = gamma f(t,x(t-1)) is considered, which leads to a resonant bifurcation of the equilibrium at critical values of the parameter. Using Floquet theory, spectral projection and center manifold reduction, we give conditions for the stability properties of the bifurcating invariant curves and four-periodic orbits. The coe±cients of the third order normal form are derived explicitly. We show that the 1:4 resonance has no e®ect on equations of the form \dot{z}(t)=-gamma r(t)g(x(t-1)).

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