Functional Derivative Analysis Distinguishes Regular and Chaotic Biological Time Series: Application to Mosquito Circadian Rhythms and Human ECG Signals

Functional derivatives are proposed as a novel quantitative tool to distinguish between regular and chaotic biological time series. Here, we analyze two distinct open-access datasets: circadian blood feeding rhythms in mosquitoes (Culex pipiens), representing a regular biological oscillator, and a human ECG signal exhibiting arrhythmia, representing a chaotic physiological system. For both, we compute the second-order functional derivative ζ(x) = f(f(x)) − f(x). We demonstrate that the mosquito feeding rhythm yields a bounded, low-variance ζ(x), indicating regularity, while the ECG signal produces large, unpredictable ζ(x) excursions characteristic of chaos. Our results show that functional derivatives can provide a sensitive measure for classifying dynamical regimes in biological systems.The author acknowledges the use of OpenAI’s language model for assistance in drafting certain sections of this work