Robust oscillatory dynamics in a mixed population of excitable and self-oscillatory Izhikevich neurons: Influence of second-order linear and nonlinear interactions.

In this study, we investigate robust oscillatory dynamics in an ensemble of excitable and self-oscillatory Izhikevich neurons subjected to higher-order interactions. Our findings reveal that, depending on the fraction of excitable neurons and the interaction strengths, bursting dynamics can emerge within the neuronal population. While linear second-order interactions tend to promote bursting behavior, nonlinear higher-order interactions show no such significant effects on the bursting region within the parameter space. Additionally, we observe spike-adding phenomena within the bursting regimes. To further explore the underlying mechanisms of the aging transition in the network, we analyze the bifurcations of a reduced model.