Analysis of a ring of mutually coupled van der Pol oscillators with coupling delay

The structure and stability of the single modes of a ring consisting of three van der Pol oscillators with coupling delay are investigated by using the nonlinear mode analysis. It is found that two single modes are stable in some intervals containing
\Delta = \pi(n'- 1), n'= 1, 2, 3,\cdots; \Delta:
delay time and that one of these modes becomes unstable for other values of A, and the relationships between the modes of oscillation and delay time are clarified. The numerical results are compared with the experimental measurements, and the satisfactory agreement is obtained between them.