Emergent synchrony, metastability, and chaos in a mixed neuronal populations with higher-order interactions

In this study, we investigate the emergent dynamics of mixed populations of self-oscillatory and excitable Izhikevich neurons embedded in a random network topology and interacting through both first-order and second-order interactions. By gradually increasing the strength of second-order interactions, we analyze its impact on synchronization, bursting dynamics, and metastability at the network level. Our results reveal a sequence of dynamical transitions from synchronized regular spiking to synchronized chaotic bursting, followed by a regime of fast chaotic spiking. The transition to chaotic bursting occurs via a spike adding route, while the subsequent transition to fast chaotic spiking is associated with the loss of the bifurcation structure responsible for burst termination, leading to the collapse of silent phases. We demonstrate that weak second-order interactions support complete cluster phase synchronization in both excitable and self-oscillatory neuronal populations, whereas increasing higher-order coupling induces a second-order transition to partially synchronized dynamics. This partially synchronized regime is characterized by synchronized bursting and metastability. Further increase in second-order interactions drives the network into a fully incoherent state characterized by irregular fast spiking. Additionally, we show that network link density strongly influences the degree of synchrony among self-oscillatory neurons but has limited impact on excitable neurons in the partial synchrony regime due to their heterogeneous firing rate distributions.