Unbounded sequences of stable limit cycles in the delayed Duffing equation: an exact analysis

Abstract

The delayed Duffing equation $${\ddot{x}}(t)+x(t-T)+x^3(t)=0$$ is shown to possess an infinite and unbounded sequence of rapidly oscillating, asymptotically stable periodic solutions, for fixed delays such that $$T^2<\tfrac{3}{2}\pi ^2$$ . In contrast to several previous works which involved approximate solutions, the treatment here is exact.