HARMONIC-BALANCE IN DELAY-DIFFERENTIAL EQUATIONS

The harmonic balance technique at first and second order is applied to three retarded delay-differential equations, comparing the results wh en possible with analytical results. For a first order equation with a fixed delay in linear and cubic terms, the first and second order har monic balance solutions are compared with an expansion of Pinney (near a bifurcation point in the coefficient of the linear term) and with a n exact solution of Dormayer. Another first order equation with a dela yed cubic term is studied, for which there is a bifurcation as the del ay increases, and a second order equation with a linear delayed term. Also the first order harmonic balance and a perturbation result for th e sunflower equation are compared. (C) 1995 Academic Press Limited