  The rapid integration of Artificial Intelligence (AI) systems across critical
domains necessitates robust security evaluation frameworks. We propose a novel
approach that introduces three metrics: System Complexity Index (SCI), Lyapunov
Exponent for AI Stability (LEAIS), and Nash Equilibrium Robustness (NER). SCI
quantifies the inherent complexity of an AI system, LEAIS captures its
stability and sensitivity to perturbations, and NER evaluates its strategic
robustness against adversarial manipulation. Through comparative analysis, we
demonstrate the advantages of our framework over existing techniques. We
discuss the theoretical and practical implications, potential applications,
limitations, and future research directions. Our work contributes to the
development of secure and trustworthy AI technologies by providing a holistic,
theoretically grounded approach to AI security evaluation. As AI continues to
advance, prioritising and advancing AI security through interdisciplinary
collaboration is crucial to ensure its responsible deployment for the benefit
of society.
