poincaré-bendixson theorem
The Poincaré-Bendixson theorem states that for a certain type of dynamical system, called a planar autonomous system, if there is a bounded trajectory (or orbit) that remains within a given region of phase space, then either the trajectory converges to an equilibrium point or it is a periodic orbit. In simple terms, this theorem helps analyze the behavior of solutions in a two-dimensional dynamical system and determine whether they approach a fixed point or cycle.
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