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

Our investigation delves into the intricate dynamical properties of a network of coupled neural oscillators, each comprising identical Jansen–Rit masses. The connections between these nodes follow the renowned Watts–Strogatz topology. Every node receives inputs from two primary sources: external and internal inputs derived from its neighboring nodes' outputs. In this paper, we aim to explore the consequences of changing these two inputs and analyze the results generated. To begin with, we analyzed the model using the mean-field approximation, assuming identical outputs across all nodes due to identical internal and external inputs. Subsequently, we relaxed this assumption, and a more detailed analysis of both states is discussed. As a result of the mean-field approach, we observed that there was no phase transition, despite apparent changes in behavior. However, the relaxation of the mean-field assumption led to the occurrence of the first (discontinuous) and second (continuous) phase transitions. Moreover, our findings indicate that by relaxing the mean-field assumption in our analysis of the single Jansen–Rit neural mass model, theta waves can be generated. Our study provides a comprehensive examination of various observed behaviors by the model, including transitions between synchrony and asynchrony. Additionally, our work highlights the potential contribution of external and internal inputs in studying phase transition and synchronization of neural mass models. Overall, our investigation sheds light on the intricate dynamics of coupled neural oscillators and their sensitivity to varying inputs. • The analysis of oscillatory behavior in a coupled nonlinear system is considered. • The change of coupling term and external input results in a transition to different dynamical states. • The first (discontinuous) and second (continuous) phase transitions result from relaxing the mean-field assumption. • Theta waves can be generated by relaxing the mean-field assumption in a single Jansen–Rit neural mass model, which has not been previously observed in a single Jansen–Rit neural mass analysis. [ABSTRACT FROM AUTHOR]