Guaranteed storing limit cycles into a discrete-time asynchronous neural network

The authors discuss a synthesis procedure of a discrete-time asynchronous neural network whose information is the limit cycle. For the synthesis procedure, they derive a condition of parameters which is necessary and sufficient for the guaranteed storing of all desired limit cycles. Also, they propose a novel connection matrix in which the upper triangle part is constructed by weighted cross-correlation and the remaining part is constructed by weighted autocorrelation. Then the synthesis procedure can be reduced to a linear equation for the weighting coefficient. If all elements of the desired limit cycles are independent at each transition step, the linear equation can be solved and all desired limit cycles can be stored. In some experiments, the procedure exhibits much better storing performance than previous ones