Bifurcation phenomena in a bi-directional coupled neural mass model

Electroencephalography (EEG) is a nonlinear dynamic complex chaotic signal. However, bifurcation analysis has been widely used as a nonlinear dynamics analysis method to explore EEG activity. We constructed a zero-delay bi-directional coupled Wendling neural mass model (BCWNMM) to simulate the functional brain network. Bifurcation analysis of the model was performed by changing the coupling strength and coupling direction to study the dynamic characteristics of the model. Finally, we used BCWNMM to simulate the EEG of epilepsy patients. Simulation results showed that when the model undergoes bidirectional coupling, various limit cycle oscillations (LCO) and bifurcation phenomena occur as the coupling coefficient changes. In addition, BCWNMM can generate epileptic-like EEG signals by adjusting the coupling strength. When the model undergoes unidirectional coupling, changes in the coupling strength cause the Wendling model of the emitting region to converge to different steady states, thereby triggering different bifurcation phenomena in the Wendling model of the receiving region. Our research results indicated that BCWNMM can generate EEG-like signals with rich dynamic characteristics, which can serve as a new method for studying the connection between two brain regions.