Theorems in dynamical systems | Stability theory

Chetaev instability theorem

The Chetaev instability theorem for dynamical systems states that if there exists, for the system with an equilibrium point at the origin, a continuously differentiable function V(x) such that 1. * the origin is a boundary point of the set ; 2. * there exists a neighborhood of the origin such that for all then the origin is an unstable equilibrium point of the system. This theorem is somewhat less restrictive than the , since a complete sphere (circle) around the origin for which and both are of the same sign does not have to be produced. It is named after Nicolai Gurevich Chetaev. (Wikipedia).

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