Every ordinary differential equation with a strict Lyapunov function is a gradient system

Abstract

We explain and prove the statement from the title. This allows us to formulate a new type of gradient inequality and to obtain a new stabilization result for gradient-like ordinary differential equations.

Keywords

• Strict Lyapunov function
• Gradient system
• Kurdyka–Łojasiewicz gradient inequality
• Convergence to equilibrium
• Damped second order ordinary differential equation