The delayed Duffing equation x''(t)+x(t-T)+x^3=0 has an infinite, unbounded sequence of exact, rapidly oscillating stable periodic solutions whenever T^2 < 3π^2/2 and the mode number is large and odd.
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Unbounded sequences of stable limit cycles in the delayed Duffing equation: an exact analysis
The delayed Duffing equation x''(t)+x(t-T)+x^3=0 has an infinite, unbounded sequence of exact, rapidly oscillating stable periodic solutions whenever T^2 < 3π^2/2 and the mode number is large and odd.