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If the equation dx/dt = f(x, y), dy/dt = g(x, y) has a locally stable equilibrium...

If the equation dx/dt = f(x, y), dy/dt = g(x, y) has a locally stable equilibrium at the origin (0, 0), does the Jacobian matrix J(x, y) satisfy: det J(0, 0) > 0, Tr J(0, 0) < 0 and why?

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