In consideration of the generation of bursts of nerve impulses (that is, rhythmic oscillation in impulse density) in the ring neural network, a synaptic modification algorithm is newly proposed. Rhythmic oscillation generally occurs in the regular ring network with feedback inhibition and in fact such signals can be observed in the real nervous system. Since, however, various additional connections can cause a disturbance which easily extinguishes the rhythmic oscillation in the network, some function for maintaining the rhythmic oscillation is to be expected to exist in the synapses if such signals play an important part in the nervous system. Our preliminary investigation into the rhythmic oscillation in the regular ring network has led to the selection of the parameters, that is, the average membrane potential (AMP) and the average impulse density (AID) in the synaptic modification algorithm, where the decrease of synaptic strength is supposed to be essential. This synaptic modification algorithm using AMP and AID enables both the rhythmic oscillation and the nonoscillatory state to be dealt with in the algorithm without distinction. Simulation demonstrates cases in which the algorithm catches and holds the rhythmic oscillation in the disturbed ring network where the rhythmic oscillation was previously extinguished.