| Abstract: |
| Many nonlinear systems exhibit oscillatory behavior in the form of limit cycles. Some common oscillator models are governed by second-order ordinary differential equations, such as the van der Pol equation. In contrast, we see that limit cycles can also be caused by delayed self-feedback within a first-order differential equation. Using perturbation methods, these ``delay limit cycle oscillators`` are shown to respond to external forcing in a similar manner to the standard ODE models.
We proceed to compare the limit cycles exhibited by these different oscillator models under various parameter choices. We explore the effect of delay and other parameters on the frequencies, phases, and amplitudes of the limit cycles, as well as on the general shape of the oscillations. Given these comparisons and features, how much can we determine about an oscillator model from a time series of its periodic orbit? |
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