  Under general conditions imposed on an active stochastic oscillator, we study
change in the size and shape of its average limit cycle as a function of
temperature. Such dynamics occur in a multitude of nonequilibrium systems,
including the spontaneous oscillations of hair cells of the inner ear. We
demonstrate one of the many mechanisms through which distortion of the mean
curve may occur and identify regions in the driven oscillator phase space
susceptible to corner-cutting due to noise. This we infer causes rounding of
certain sharp features in the noiseless curve given by the underlying complex
theoretical model, making them inaccessible under any amount of averaging of
the experimentally obtained finite-temperature trajectory.
