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arXiv · 1908.06533

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

Si Mohamed Sah·Bernold Fiedler·B. Shayak·Richard H. Rand
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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.

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Si Mohamed Sah, Bernold Fiedler, B. Shayak, Richard H. Rand. 2019-08-18. Unbounded sequences of stable limit cycles in the delayed Duffing equation: an exact analysis. https://arxiv.org/abs/1908.06533

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