The exponentially decaying tabu search, which exhibits high performance in solving quadratic assignment problems (QAPs), has been implemented on a neural network with chaotic neurodynamics. To exploit the inherent parallel processing capability of analog hardware systems, a synchronous updating scheme, in which all neurons in the network are updated simultaneously, has also been proposed. However, several neurons may fire simultaneously with the synchronous updating. As a result, we cannot determine only one candidate for the 2-opt exchange from among the many fired neurons. To solve this problem, several neuron selection methods, which select a specific neuron from among the fired neurons, have been devised. These neuron selection methods improved the performance of the synchronous updating scheme; however, the dynamics of the chaotic neural network driven by these heuristic algorithms cannot be intuitively understood. In this paper, we analyze the dynamics of a chaotic neural network driven by the neuron selection methods by considering the spatial and temporal mutual information.