Dynamics of mixed bursting in coupled pre-Bötzinger complex

Abstract

The pre-Bötzinger complex, which is located at a ventrolateral medulla of human and mammal, is considered to be the center for the generation of respiratory rhythms. In a normal state, the respiratory rhythm is uniform and orderly. Otherwise, the respiratory rhythm will change to a pathological state. Therefore, the monitoring of respiratory rhythm is of great significance in monitoring the health. In this paper, according to a two-coupled model of pre-Bötzinger complex with calcium ion current, we investigate the generation and transition mechanism of anti-phase bursting synchronization by using phase-plane analysis, bifurcation and fast-slow decomposition. It is found that the pre-Bötzinger complex model can exhibit mixed bursting when calcium ion concentration is at steady state, which indicates that the oscillation of calcium is not a necessary condition for the generation of mixed bursting. This is quite different from the results obtained in previous studies, indicating that the mixed bursting is caused by the periodic fluctuations of calcium. The methods used in this paper can provide a new idea for investigating the dynamics of mixed bursting, and it can also be applied to the study of other neuronal systems on a multiple time scale.

Equation of state and anisotropy of pressure of magnetars

“…The relativistic mean field theory (RMFT) is a standard method for studying the properties of finite nuclear matter. The TMA parameter set is consistent with the predictions of relativistic Brueckner‐Hartree‐Fock theory, and can describe well the EoS of NSs (Gao et al 2017a; Geng et al 2005; Sugahara & Toki 1994; Wei et al 2006; Zhao et al 2021; Zhao et al 2022a; Zhao et al 2022b; Zhao & Tang 2022). In this paper, we will solve the general relativistic hydrostatic equilibrium equation and study how a strong magnetic field affects the EoS of an NS by combining the TMA parameter set in the RMFT framework.…”

“…Even some authors showed that a possibility that a strong magnetic field is produced by color ferromagnetic quark matter in NSs (Dong et al 2013; Kozhberov & Yakovlev 2020). Given the great importance of magnetars in astrophysics, here we will explore the EoSs as well as the anisotropy of pressure of magnetars (Li & Gao 2023; Wang et al 2022; Zhao et al 2021). This work is organized as follows.…”

Non-Smooth Dynamic Behaviors as well as the Generation Mechanisms in a Modified Filippov-Type Chua’s Circuit with a Low-Frequency External Excitation

“…A novel bursting form named mixed bursting oscillation has been observed in [18], which is characterized by the fact that different SP patterns can be performed in a period bursting oscillation. By using slow-fast decomposition, Duan et al pointed out that different bistability structures may lead to different mixed bursting patterns [19].…”

Slow–Fast Dynamics Behaviors under the Comprehensive Effect of Rest Spike Bistability and Timescale Difference in a Filippov Slow–Fast Modified Chua’s Circuit Model

“…[20], where the trajectory can perform different SP patterns in a complete periodic motion. Duan et al point out that such a special bursting pattern can be explained by bistability structures in the fast subsystem [21]. In continuous slow-fast dynamical systems, the slow-fast dynamic behaviors as well as the generation mechanisms are well understood based on slow-fast decomposition and the relatively well-developed conventional dynamics theories [22].…”