Stability Theory is a branch of mathematics that studies the behavior of systems in response to small disturbances. It helps determine whether a system will return to its original state after a change or if it will diverge into a different state. This theory is widely applied in various fields, including engineering, economics, and ecology. In the context of dynamical systems, Stability Theory often involves analyzing equilibrium points. An equilibrium point is stable if nearby trajectories converge to it over time. Conversely, if trajectories move away from the equilibrium, it is considered unstable. This concept is crucial for understanding the long-term behavior of systems in physics and control theory.