Search

Bursting is a crucial form of firing in neurons, laden with substantial information. Studying it can aid in understanding the neural coding to identify human behavioral characteristics conducted by these neurons. However, the high-dimensionality of many neuron models imposes a difficult challenge in studying the generative mechanisms of bursting. On account of the high complexity and nonlinearity characteristic of these models, it becomes nearly impossible to theoretically study and analyze them. Thus, this paper proposed to address these issues by focusing on the midbrain dopamine neurons, serving as the central neuron model for the investigation of the bursting mechanisms and bifurcation behaviors exhibited by the neuron. In this study, we considered the dimensionality reduction of a high-dimensional neuronal model and analyzed the dynamical properties of the reduced system. To begin, for the original thirteen-dimensional model, using the correlation between variables, we reduced its dimensionality and obtained a simplified three-dimensional system. Then, we discussed the changing characteristics of the number of spikes within a burst by simultaneously varying two parameters. Finally, we studied the co-dimension-2 bifurcation in the reduced system and presented the bifurcation behavior near the Bogdanov-Takens bifurcation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Many types of neurons and excitable cells could intrinsically generate bursting activity, even in an isolated case, which plays a vital role in neuronal signaling and synaptic plasticity. In this paper, we have mainly investigated bursting types and corresponding bifurcations in the pre-Bötzinger complex respiratory rhythm neuron by using fast-slow dynamical analysis. The numerical simulation results have showed that for some appropriate parameters, the neuron model could exhibit four distinct types of fast-slow bursters. We also explored the bifurcation mechanisms related to these four types of bursters through the analysis of phase plane. Moreover, the first Lyapunov coefficient of the Hopf bifurcation, which can decide whether it is supercritical or subcritical, was calculated with the aid of MAPLE software. In addition, we analyzed the codimension-two bifurcation for equilibria of the whole system and gave a detailed theoretical derivation of the Bogdanov-Takens bifurcation. Finally, we obtained expressions for a fold bifurcation curve, a nondegenerate Hopf bifurcation curve, and a saddle homoclinic bifurcation curve near the Bogdanov-Takens bifurcation point. [ABSTRACT FROM AUTHOR]

Electrical bursting is an activity which is universal in excitable cells such as neurons and various endocrine cells, and it encodes rich physiological information. As burst delay identifies that the signal integration has reached the threshold at which it can generate an action potential, the number of spikes in a burst may have essential physiological implications, and the transition of bursting in excitable cells is associated with the bifurcation phenomenon closely. In this paper, we focus on the transition of the spike count per burst of the pancreatic -cells within a mathematical model and bifurcation phenomenon in the Chay-Keizer model, which is utilized to simulate the pancreatic -cells. By the fast-slow dynamical bifurcation analysis and the bi-parameter bifurcation analysis, the local dynamics of the Chay-Keizer system around the Bogdanov-Takens bifurcation is illustrated. Then the variety of the number of spikes per burst is discussed by changing the settings of a single parameter and bi-parameter. Moreover, results on the number of spikes within a burst are summarized in ISIs (interspike intervals) sequence diagrams, maximum and minimum, and the number of spikes under bi-parameter value changes. [ABSTRACT FROM AUTHOR]