Hyperbolic equilibrium point

In dynamical systems, an equilibrium point is a point where the system can remain indefinitely if it starts there, assuming no external disturbances. An equilibrium point is classified based on its stability properties, which are determined by analyzing the behavior of the system near that point. A **hyperbolic equilibrium point** is a specific type of equilibrium point where the linearization of the system at that point has no eigenvalues with zero real parts.