We propose a neurodynamical approach to a large scale optimization problem in the Cognitive Wireless Clouds, in which a huge number of mobile terminals with multiple different air interfaces autonomously utilize the most appropriate infrastructure wireless networks, by sensing available wireless networks, selecting the most appropriate one, and reconfiguring themselves with seamless handover to the target networks. In order to deal with such a cognitive radio network, the game theory has been applied in order to analyze stability of the dynamical systems consisting of the mobile terminals' distributed behaviours, but it is not based on fundamental optimization property. As more natural optimization dynamical system model suitable for large-scale complex systems, we introduce the mutual connection neural network dynamics which converges to an optimal state with always decreasing property of its energy function. In this paper, we apply such a neurodynamics to optimization problem in radio access technology selection. We composed a neural network which solves the problems, and showed that it is possible to improve total average throughput only by distributed and autonomous neuron updates on the terminal side.