In mathematics, the Bendixson–Dulac theorem on dynamical systems states that if there exists a C 1 {\displaystyle C^{1}} function φ {\displaystyle \varphi } such that the expression ∂ ∂ x + ∂ ∂ y {\displaystyle {\frac {\partial }{\partial x}}+{\frac {\partial }{\partial y}}} has the same sign almost everywhere in a simply connected region of the plane, then the plane autonomous system d x d t = f, {\displaystyle {\frac {dx}{dt}}=f,} d y d t = g {\displaystyle {\frac {dy}{dt}}=g} has no nonconstant periodic solutions lying entirely within the region. Wikipedia