Hidden complexity of biological clocks that adapt to external control and internal regulation: a case study on body temperature simulation

Using the Duffing equation to model body temperature's circadian rhythms, we simulated four cases with varying driving force parameters γ (0.32, 0.33, 0.34, and 0.35). We compared these simulations to published experimental data using Fourier and entropy analyses along Poincaré sections. For normal work-sleep conditions (γ = 0.35), the system showed precise resetting at specific times. Under shift work conditions (γ = 0.34), resetting behavior was reduced, causing a phase shift in the rhythm. Long-term constant temperature conditions (γ = 0.33) displayed a reset at the period's start, similar to normal conditions. With no external driving forces (γ = 0.32), multiple resets occurred within the period, emphasizing the need for frequent resets to maintain stability. The simulation results align partially with experimental data, highlighting the system's adaptability to external changes.