Consider a general 2D system:

x' = f(x,y)

y’ = g(x,y)

Do you know any such system which has a limit cycle while there is no equilibrium in it? For example the famous Van Der Pol is not an answer; Because, although it has a limit cycle, it has an equilibrium in the origin (0,0)

x' = y

y’ = ay(1-x^2)-x

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