By rescaling the system，we obtain the Lorenz-Stenflo system with slow variation of the flow rotation. Based on Routh-Hurwitz criteria，the stabilities of the equilibria are analyzed and the bifurcation sets are sought to divide the parameter plane into different regions，corresponding to different types of the solutions. Different types of the solutions may bifurcate from the equilibria with the chang of the parameters. Furthermore，the symmetric bursting and the symmetric chaos are presented，and the mechanism of the symmetric bursting is explored by the method of slow-fast analysis.