First-order Euler method is effective for computation of associative-memory network of Kuramoto oscillators

We consider the Kuramoto-type models for associative-memory networks and its applications in binary pattern retrieval and classification. In this model, the coupling function consists of a Hebbian term and a second-order Fourier term with nonnegative parameter. The theory of the stability/instability has been established in literature for the equilibria corresponding to binary patterns. In this short communication, we investigate the computation method of this model. In practical situations, quick-response is highly desired. However, as the size of the network increases, the high dimension causes heavy computation cost, and even a curse of dimensionality. We provide the discrete-time formulation given by the first-order Euler method, and show that this method is effective in the computation of the continuous-time model. This simplifies the computation and simulations verify that the computation cost is reduced, comparing to the conventional higher-order Runge–Kutta method.