Mathematical Modeling Using Gaussian Functions and Chaotic Attractors: A Hybrid Approach for Realistic Representation of the Intrinsic Dynamics of Heartbeats

Background: Realistic simulation of ECG signals is essential for validating signal-processing algorithms and training artificial intelligence models in cardiology. Many existing approaches model either waveform morphology or heart rate variability (HRV), but few achieve both with high accuracy. This study proposes a hybrid method that combines morphological accuracy with physiological variability. Methods: We developed a mathematical model that integrates Gaussian mesa functions (GMF) for waveform generation and a chaotic Rössler attractor to simulate RR-interval variability. The GMF approach allows fine control over the amplitude, width, and slope of each ECG component (P, Q, R, S, T), while the Rössler system introduces dynamic modulation through the use of seven parameters. Spectral and statistical analyses were applied, including power spectral density (PSD) computed via the Lomb–Scargle, STFT, CWT, and histogram analyses. Results: The synthesized signals demonstrated physiological realism in both the time and frequency domains. The LF/HF ratio was 1.5–2.0 when simulating a normal rhythm and outside these limits in a simulated stress rhythm, consistent with typical HRV patterns. PSD analysis captured clear VLF (0.003–0.04 Hz), LF (0.04–0.15 Hz), and HF (0.15–0.4 Hz) bands. Histogram distributions showed amplitude ranges consistent with real ECGs. Conclusions: The hybrid GMF–Rössler approach enables large-scale ECG synthesis with controllable morphology and realistic HRV. It is computationally efficient and suitable for artificial intelligence training, diagnostic testing, and digital twin modeling in cardiovascular applications.