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In this paper, we apply distributed optimization dynamics of the mutually connected neural networks to RAN selection in heterogeneous type cognitive wireless networks. We evaluate the performance of the proposed approach by implementing it on an experimental heterogeneous wireless network system called Cognitive Wireless Cloud, which supports vertical handover between different radio access networks and various information exchange defined in IEEE1900.4. Our neural algorithm implemented on such an experimental wireless network optimizes objective function without any centralized computation. As the objective functions, we introduce two types of problems, load balancing and QoS satisfaction rate optimization, and compare the performance of the proposed method with those of other distributed RAN selection algorithms on the real wireless system. The experimental results using such a system show that the proposed algorithm exhibits the best performance. Since our algorithm based on the neural network dynamics directly optimizes the objective functions defined for radio resource usage optimization of the entire wireless network by distributed computation on each terminal, its performance becomes better than other algorithm which is based on the improvement of each terminal's QoS.