ABSTRACT
Previous work has investigated the dynamics of two weakly coupled van der Pol oscillators in which the coupling terms have time delay [7], [8], [9], [10]. The coupling was chosen to be via the first derivative terms because this form of coupling occurs in radiatively coupled microwave oscillator arrays [2], [3], [12], [13]. The method of averaging was used to obtain an approximate simplified system of three slow flow equations and then the terms with the time delay were approximated via a Taylor series expansion. It was also predicted that the stability curves for the in-phase and out-of-phase modes are periodic in the delay. Numerical integration of the original system showed that the approximated system agrees well when certain parameters are small and begins to break down for larger parameter values. Work on other models with time delay found non-periodic dependence of the bifurcation curves on
the time delay [4], [5], [6], [11]. This current work examines the averaged equations before they have been Taylor expanded and then investigates the stability and bifurcation of their equilibria. These bifurcation curves are compared with those obtained with the Taylor series truncation and the validity of the original results is examined.
