Reduced and bifurcation analysis of intrinsically bursting neuron model

Intrinsic bursting neurons represent a common neuronal type that displays bursting patterns upon depolarization stimulation. These neurons can be described by a system of seven-dimensional equations, which pose a challenge for dynamical analysis. To overcome this limitation, we employed the projection reduction method to reduce the dimensionality of the model. Our approach demonstrated that the reduced model retained the inherent bursting characteristics of the original model. Following reduction, we investigated the bi-parameter bifurcation of the equilibrium point in the reduced model. Specifically, we analyzed the Bogdanov-Takens bifurcation that arises in the reduced system. Notably, the topological structure of the neuronal model near the bifurcation point can be effectively revealed with our proposed method. By leveraging the proposed projection reduction method, we could explore the bursting mechanism in the reduced Pospischil model with greater precision. Our approach offers an effective foundation for generating theories and hypotheses that can be tested experimentally. Furthermore, it enables links to be drawn between neuronal morphology and function, thereby facilitating a deeper understanding of the complex dynamical behaviors that underlie intrinsic bursting neurons.