Nonlinear Dynamic Modeling and Stability-Driven Optimization of Trust Mechanisms in Fog Computing Networks

Abstract

Trust management in fog computing networks supporting real-time healthcare applications exhibits inherently nonlinear behavior due to bounded trust constraints, adversarial perturbations, and load-dependent saturation effects. In this work, we develop a nonlinear dynamical system model describing the evolution of trust in distributed fog environments. The proposed framework formulates trust dynamics using nonlinear differential equations incorporating reinforcement mechanisms, adversarial degradation, and quadratic saturation terms. Equilibrium points are derived analytically, and both local and global stability conditions are established using Lyapunov theory. We further investigate parameter-induced bifurcation behavior and identify thresholds under which adversarial influence dominates system stability. A fourth-order Runge–Kutta scheme is employed to validate the model numerically, and conver-
gence properties are formally discussed. The results demonstrate that nonlinear modeling provides deeper insight into resilience characteristics of fog-based trust systems and offers rigorous mathematical guarantees for stability under adversarial conditions. The developed framework bridges nonlinear analysis and secure fog computing, contributing to mathematically grounded cybersecurity modeling.