In this article a neural network model with transient chaos and time-variant gain is proposed.By introducing transiently chaos and time-valiant gain

the proposed neural neira; metwork has richer and more flexible dynamics rather than Hopfield-like neural networks only with POint attractors

so that it can be expected to have higher ability of searching for globally optimal or near-optimal solutions. After going through an inversebifurcation process

the neural network gradually approaches to a conventional Hopfield netal network stalting from a good initial state. It can be used to solving various complicated optimization problem and associative memories. Extensive numerical simlilations show that the network would not be stuck into local minima. Finally

we applied the network to maximum likelihood direction estimation of spatial signal sources.