Consider the system:(adsbygoogle = window.adsbygoogle || []).push({});

dx/dt = y, dy/dt = 2x - 4x^{3}- y.

I know that the Hamiltonian H(x,y) = y^{2}/2 - x^{2}+ x^{4}+ y^{2}/2 = y^{2}- x^{2}+ x^{4}. But how do I show that H is a Lyapunov function for this system. Please help.

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# Dx/dt = y, dy/dt = 2x - 4x

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