Finding a Lyapunov function for a given system

ordinary-differential-equations stability-in-odes

Solution 1:

As explained in the comments, even though simulated phase diagrams seem to exhibit cycling trajectories near the origin, they are not conclusive enough to decide whether the origin is stable or not, that is, whether trajectories cycle or spiral outwardly or spiral inwardly. Caution is advised about approximation errors in simulations.

streamplot{{-2x^4+y,-2x-2y^6},{x,-1,1},{y,-1,1}}

enter image description here

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