UC Santa Barbara

A key consideration for nonlinear oscillators is how they respond to parametric perturbations; such changes in parameters can often lead to effects on both the amplitude and phase of these oscillators. When the underlying process is sensitive to these changes, there may be large effects on the system leading to unwanted conditions. Additionally, models for nonlinear oscillators are often high-dimensional and intractable, making analysis in terms of the original coordinates nonintuitive. Utilizing an isostable and isochron coordinate frame, the transient dynamics of nonlinear oscillators to parametric perturbations can be analyzed in a convenient way by making use of the phase and impulse response curves from augmented phase reduction. Although isochron and isostable coordinates are convenient to use in analysis, typically one is interested in understanding what happens in terms of the original variables, and thus, a coordinate recovery framework is devised to take the results from the isostable and isochron frame back to the original coordinates. This approach shows great promise for understanding the transient behavior of nonlinear oscillators due to parametric perturbations.