Abstract: The accurate computation for getting ramification of algebra iterated system was studied by the analysis of the double period bifurcation of Logistic dynamic mapping system with ecological characteristic. Regarding iterated processes as objective function, parameters of algebra iterated system as design variables, and boundary condition of iterated variables as constrains, a new optimum method was proposed. The method was used to calculate bifurcation algebra iterated mapping. Turning constrains into punishing items, the punishing function method was used to deal with the optimum problem, and accurate results were acquired. The method can solve ramification of algebra iterated system rapidly and exactly.