A neuron model with fluid properties for solving labyrinthian puzzle

Abstract

Hopfield presented a neural network with continuous states, associated with an analogue circuit (1984). On the condition that the weights keep $T_{ii} = - \sum {_{j \ne i} {\text{T}}_{ij} }$ and $T_{ii} = T_{ji} \geqslant 0$for i≠j, the potential u _iof the neurons in the system can be of the properties like those of fluid and the communication among neurons is the result of the flowing of the potential like the flowing of fluid (ideal liquid) affected only by gravity. This means that the flowing of the potential among neurons is from higher level to lower level and that the cause for the varing of a neuron in its state is due to that the net input flowrate of all the potential to the neuron is nonzero. Therefore, the system has a quite clear convergent process and, has a unique stable state. Analysing the possible stable state of the system is based on both the flowrate rule and the invariability in volume satisfied by the potential. The experiment of solving labyrinthian puzzle shows that the neural system with fluid properties is well-done to intelligence search problem.