Block Diagram Analysis of a Design Principle for Amplitude-Frequency Profiles in Biological Oscillations

An important design principle for biological oscillators divides the oscillators into two classes: fixed frequency, variable amplitude and fixed amplitude, variable frequency. Because of the interplay of nonlinearity and feedback, both positive and negative, analytical investigations of this design principle are primarily based on numerical simulations of ordinary differential equations. To enhance the qualitative and quantitative characterization, we adapted and developed a block diagram modeling framework. We showed how the observed amplitude-frequency characteristics could be obtained from the block diagram models. We obtained constraints on the positive feedback and negative feedback strengths for the oscillations to exist. These results should contribute to a systems and control perspective on oscillations in biology and related contexts.