This letter studies the simple dynamic binary neural network characterized by signum activation function and ternary connection parameters. In order to control the sparsity of the connections and the stability of the stored signal, a simple evolutionary algorithm is presented. As a basic example of teacher signals, we consider a binary periodic orbit which corresponds to a control signal of ac-dc regulators. In the numerical experiment, applying the correlation-based learning, the periodic orbit can be stored. The sparsification can be effective to reinforce the stability of the periodic orbit.