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In this paper,the theories of multiple limit cycles and bifurcation for 4 dimensional circular truss for large-scale space deployable antenna under the 1∶2 internal resonance is studied.Based on average theory and brouwer degree theory,we study the bifurcation of multiple limit cycles parametrical conditions,upper bounds of the number and relative position relationships for antenna system which is perturbed by its linear,quadratic and cubic nonlinear polynomials.