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