Generalising the Kuramoto model for the study of neuronal synchronisation in the brain (Q869705)

The paper presents a numerical analysis of the coupled system \[ \dot \theta_i = \omega_i(t) + \frac{1}{N} \sum_{j=1}^N K_{i,j}(t) \sin (\theta_j-\theta_i), \quad i=1,\dots,4, \] which is a generalization of the Kuramoto system to the case of time-dependent frequencies \(\omega_i(t)\), and coupling \(K_{i,j}(t)\). The authors study the behavior of the order parameter \(re^{i\psi}=(1/N)\sum_{j=1}^N e^i\theta_j\) for different cases of \(K_{i,j}(t)\), corresponding to different connection architectures, such as linear array, ring, or all-to-all.