Dynamical analysis of spontaneous Ca<sup>2+</sup> oscillations in astrocytes

Yapeng Zhang; Yu Chen; Quanbao Ji; Yapeng Zhang; Yu Chen; Quanbao Ji

doi:10.3934/era.2024020

Electronic Research Archive

2024, Volume 32, Issue 1: 405-417. doi: 10.3934/era.2024020

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Dynamical analysis of spontaneous Ca²⁺ oscillations in astrocytes

1.
School of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, China
2.
Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning 530006, China

Received: 27 September 2023 Revised: 08 December 2023 Accepted: 20 December 2023 Published: 28 December 2023

In this work, we focus on a nonlinear dynamical model proposed by Lavrentovich et al. to compute and simulate spontaneous Ca²⁺ oscillations evoked by calcium ion efflux in astrocytes. Selected parameters are chosen, with observation of periodic and chaotic Ca²⁺ oscillations in cytosol. The stability analysis of equilibrium is conducted using the center manifold theorem to investigate the dynamics underlying spontaneous Ca²⁺ oscillations in astrocytes. The results indicate that the Hopf bifurcation represents the dynamical changes in stability of spontaneous Ca²⁺ oscillations. In addition, numerical simulations are performed to further assess the validity of the aforementioned analysis.
- astrocytes,
- Hopf bifurcation,
- center manifold,
- stability
Citation: Yapeng Zhang, Yu Chen, Quanbao Ji. Dynamical analysis of spontaneous Ca2+ oscillations in astrocytes[J]. Electronic Research Archive, 2024, 32(1): 405-417. doi: 10.3934/era.2024020

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Abstract

In this work, we focus on a nonlinear dynamical model proposed by Lavrentovich et al. to compute and simulate spontaneous Ca²⁺ oscillations evoked by calcium ion efflux in astrocytes. Selected parameters are chosen, with observation of periodic and chaotic Ca²⁺ oscillations in cytosol. The stability analysis of equilibrium is conducted using the center manifold theorem to investigate the dynamics underlying spontaneous Ca²⁺ oscillations in astrocytes. The results indicate that the Hopf bifurcation represents the dynamical changes in stability of spontaneous Ca²⁺ oscillations. In addition, numerical simulations are performed to further assess the validity of the aforementioned analysis.

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