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Differential EquationsMediumNonlinear Systems & Linearization

Nonlinear Systems & Linearization · Medium problem

Consider the gradient system x′=−∂U∂x,  y′=−∂U∂yx' = -\dfrac{\partial U}{\partial x},\; y' = -\dfrac{\partial U}{\partial y} with U(x,y)=x4−2x2+y2U(x, y) = x^4 - 2x^2 + y^2. How many of its equilibria are asymptotically stable?