Analytical Method for Stroboscopically Sampling General Periodic Functions with Arbitrary Frequency Sweep Rates

Parameter sweeps are commonly used to explore the behavior of dynamical systems. This paper derives exact solutions for the instances in time to stroboscopically sample the response of a dynamical system subject to varying input excitations. This work will enable more accurate bifurcation diagrams and Poincare sections in parameter regimes where numerical approaches may lead to incorrect behavior characterization. The simplest case of a linear frequency sweep is first considered before generalizing the results to include more complex functions with nonlinear sweep rates and arbitrary phase shifts.

Duke Scholars

Author Brian Mann Thomas Lord Department of Mechanical Engineering and Materia ...