Gradient systems have some particularly simple properties. They cannot exhibit oscillatory behaviour and their stability can be investigated using a natural Lyapunov function that can always be found by integration. An arbitrary dynamic system can be represented as the sum of a gradient system and a conservative system. An analysis of the system in its decomposed form is shown to lead to a Lyapunov-like algorithm. The algorithm can be applied to yield directly a graphical indication of the qualitative behaviour of nonlinear second-order systems.
Gradient systems and system decomposition, Page 1 of 2
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