This work considers the placement of unmanned aerial vehicle base stations (UAV-BSs) with criterion of minimum UAV-recall-frequency (UAV-RF), indicating the energy efficiency of mobile UAVs networks. Several different power consumptions, including signal transmit power, on-board circuit power and the power for UAVs mobility, and the ground user density are taken into account. Instead of conventional empirical stochastic models, this paper utilizes a pattern formation system to track the instable and non-ergodic time-varying nature of user density. We show that for a single time-slot, the optimal placement is achieved when the transmit power of UAV-BSs equals their on-board circuit power. Then, for multiple time-slot duration, we prove that the optimal placement updating problem is a nonlinear dynamic programming coupled with an integer linear programming. Since the original problem is NP-hard and can not be solved with conventional recursive methods, we propose a sequential-Markov-greedy-decision method to achieve near minimal UAV-RF in polynomial time. Further, we prove that the increment of UAV-RF caused by inaccurate predicted user density is proportional to the generalization error of learned patterns. Here, in regions with large area, high-rise buildings or low user density, large sample sets are required for effective pattern formation.