Unified framework for combined practical and Hyers–Ulam stability of impulsive gene regulatory networks

This paper establishes a unified stability framework integrating practical stability (PS) and Hyers–Ulam stability (HUS) for impulsive gene regulatory networks (GRNs) with distributed delays. We propose novel mathematical formulations that simultaneously guarantee biological states remain within practically acceptable bounds (PS) while maintaining robustness against model uncertainties and disturbances (HUS). Through Lyapunov-based impulsive controllers, we demonstrate how this integrated approach provides superior reliability for biological implementations compared to single-method stability criteria. Numerical simulations validate the framework’s efficacy in oncogene regulation scenarios, showing 100% adherence to safety constraints despite 15% model uncertainties. The combined PS–HUS paradigm offers transformative potential for synthetic biology and precision medicine applications.