Linear and nonlinear stability analysis

Linear stability analysis examines how small deviations or disturbances in a system evolve over time by approximating the system's behavior using linear equations. If these disturbances diminish, the system is stable; if they grow, it is unstable. Nonlinear stability analysis, on the other hand, considers the system's full complexity without simplifying assumptions, addressing how larger disturbances or the system's inherent nonlinearities affect its long-term behavior. It provides a deeper understanding of stability but is often more mathematically challenging. Together, they help predict whether a system will maintain its state or change significantly under different conditions.