In the three-dimensional space Elesclomol simulation, the order parameter (which is also the control) ψψ within co-evolution to a certain extent explains the macro-process in which technological network and social network engage in co-evolution in the cooperative network with knowledge flow under strategic alliances. This study solves order parameters with a symmetric matrix; hence, in order to highlight the differences of the co-evolution between technological network and social network among different resource allocation patterns, we use a two-dimensional projection to obtain the result of the order parameter’s three-dimensional simulation in the collaborative evolution under different patterns. Moreover, we introduce two concepts which observe the evolution rule of the order parameter, namely density functions and vector fields. By analyzing the value distribution area and changes of the density function and vector field, we summarize the characteristics of co-evolution of a technological network and a social network within a cooperative network with knowledge flow under strategic alliance. The density function presents the status of the order parameter distribution under the proposed four types of resource allocation patterns. The result is higher at deeper areas, which indicates that the rate of evolution in the area is relatively fast.
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