On the influence of input triggering on the dynamics of the Jansen-Rit oscillators network

We investigate the dynamical properties of a network of coupled neural oscillators with identical Jansen-Rit masses. The connections between nodes follow the regular Watts-Strogatz topology. Each node receives deterministic external input plus internal input based on the output signal from the neighbors. This paper aims to change these two inputs and analyze the generated results. First, we attempt to analyze the model using the mean-field approximation, i.e., identical inputs for all nodes. Then, this assumption is relaxed. A more detailed analysis of these two states is discussed. We use the Pearson correlation coefficient to measure the amount of synchronization. As a result of the mean-field approach, we find that despite observed changes in behavior, there is no phase transition. Surprisingly, both the first (discontinuous) and second (continuous) phase transition occurs by relaxing the mean-field assumption. We also demonstrate how changes in input can result in pathological oscillations similar to those observed in epilepsy. Results show that coupled Jansen-Rit masses emerge a variety of behaviors influenced by various external and internal inputs. Moreover, our findings indicate that delta waves can be generated by altering these inputs in a network of Jansen-Rit neural mass models, which has not been previously observed in a single Jansen-Rit neural mass model analysis. \\ Overall, a wide range of behavioral patterns, including epilepsy, healthy behavior, and the transition between synchrony, and asynchrony are examined comprehensively in this paper. Moreover, this work highlights the putative contribution of external and internal inputs in studying the phase transition and synchronization of neural mass models.