  We investigate the dynamics of a delay differential coupled Duffing-Van der
Pol oscillator equation. Using the Lindstedt's method, we derive the in-phase
mode solutions and then obtain the slow flow equations governing the stability
of the in-phase mode by employing the two variable perturbation method. We
solve the slow flow equations using series expansion and obtain conditions for
Hopf bifurcation and studied stability of the in-phase mode. Finally, we
studied stability and bifurcations of the origin. Our interest in this system
is due to the fact that it is related to the coupled laser oscillators.
