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We discuss a new type of delay differential equation that exhibits resonatingtransient oscillations. The power spectrum peak of the dynamical trajectoryreaches its maximum height when the delay is suitably tuned. Furthermore, ouranalysis of the resonant conditions for this equation has revealed a newconnection between the solutions of the transcendental trigonometric equationand the Lambert W function. These results offer fresh insights into thenonlinear dynamics induced by delayed feedback.

Delay, resonance and the Lambert W function