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Exercise : Consider the dynamical system : $$x' = -x +y^3$$ $$y' = -y+ax^3$$ with $(x,y) \in \mathbb R^2$. Find the stationary point of the system and study their stability for every value of $a$. Show that if $a=1$ and $V(x,y) \leq R$, where $R>0$ is a constant and \$V(x,y) = \frac{1}{2...