The Poincaré-Bendixson Theorem is a fundamental result in the theory of dynamical systems that provides conditions under which a certain type of behavior occurs in two-dimensional systems. Specifically, it states that if a trajectory of a continuous dynamical system in the plane remains in a compact region and does not approach any equilibrium point, then it must approach a periodic orbit. This theorem plays a significant role in understanding the long-term behavior of nonhomogeneous systems and stability analysis.
congrats on reading the definition of Poincaré-Bendixson Theorem. now let's actually learn it.