In the real world, condensation based on preferential aggregate mechanism, such as migration-driven aggregate growth system and packets routing in complex networks, is an important phenomenon. The research studies the ZRP condensation based on preferential aggregate mechanism in sale-free networks, in order to understand how the weighted transport with preferential hopping rates influences real systems. Instead of the approach of grand canonical ensemble which is generally used in a zero range process, an alternate approach of the mean field equations is used to study the dynamics of ZRP. The research finds that there are three phases when preferential aggregate index is greater than zero: namely the complete condensation, partial condensation, and well-proportioned condensation. But the ZRP system has only two phases when the preferential aggregate index is smaller than zero:the partial condensation and well-proportioned condensation. On the other hand, the mean particle distribution in the stationary state depends on the jumping rate, link weight, and preferential aggregate indexes. Monte Carlo simulation also validates the analytical results.
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