Dynamics Analysis of Chaotic Equations in Coronary Arteries

The study presents a unified Duffing-type framework to analyze how physiological perturbations can cause irregular wall motions in coronary arteries. The model incorporates linear and nonlinear wall recoil, flowmediated feedback, viscoelastic (derivative) coupling, periodic cardiaclike forcing, singular constriction terms that mimicking nearocclusive narrowing, and saturating compliance. Direct numerical simulationsincluding phase portraits, Poincar sections, and longtime integrationscorroborate this theory: unforced systems relax regularly into single or doublewell equilibria, whereas modest periodic inputs tuned near Melnikov thresholds produce interwell transport, thickened invariantset remnants, broadband Poincar scattering, and intermittent largeamplitude wall excursions. Extended Stype formulations featuring singular and saturating terms further enrich the route to chaos and highlight the sensitizing role of viscoelastic memory. This framework establishes a mathematically transparent bridge between vascular biomechanics and nonlinear dynamical diagnostics, suggesting earlywarning metrics for transition to pathological oscillations in coronary vessels.