Abstract

C o m m e n t o n th e C h a o tic B e h a v io u r o f v a n d e r P o l E q u a tio n s w ith a n E x t e r n a l P e rio d ic E x c ita tio n The limit cycle system with an external periodic force d2u/df2 — a(1 — u2)du/dt + u" -/ccos(ßf) (n = 1, 3, 5,...) can show chaotic behaviour for certain values of a, k and Q. We study the influence of n on the chaotic behaviour. For n = 1 we select values which result in chaotic motion of the system. Then we investigate the behaviour of the system for n = 3, 5 and 7. Introducing the nonlinearity u"(n — 3, 5, 7) gives the surprising result that the chaotic motion ceases to exist. It is well known that the differential equation