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"Stability Analysis" as a book category covers the theory, methods, and applications used to determine whether systems—mathematical, physical, biological, economic, or engineered—remain near a desired state under perturbations. Books in this category typically develop foundational concepts (equilibria, attractors, Lyapunov functions, linearization, bifurcation, robustness), present analytical and numerical techniques (eigenvalue methods, input-to-state stability, stochastic stability, sensitivity and perturbation analysis), and demonstrate practical tools for model-based assessment and design. They range from rigorous mathematical treatments for researchers to applied texts for engineers and scientists, often including case studies and software implementations for control systems, power grids, structures, ecosystems, and financial models. Overall, the genre emphasizes understanding how and why systems maintain, lose, or recover stability and how to quantify and improve resilience in real-world settings.

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