Linear stability theory

Linear stability theory is a way to analyze whether small disturbances in a system, like a fluid flow or a structure, will die out or grow over time. It involves mathematically simplifying complex behaviors by approximating responses to tiny changes. If these small disturbances tend to diminish, the system is considered stable; if they grow, it’s unstable. This theory helps engineers and scientists predict system behavior, design safer structures, and understand phenomena like turbulence or vibrations, by focusing on how minor deviations influence the overall stability of the system.