Computational Analysis and Bifurcation of Regular and Chaotic Ca 2+ Oscillations

Xinxin Qie and Quanbao Ji
Additional contact information
Xinxin Qie: School of Mathematics and Physics, Guangxi University for Nationalities, Nanning 530006, China
Quanbao Ji: School of Mathematics and Physics, Guangxi University for Nationalities, Nanning 530006, China

Mathematics, 2021, vol. 9, issue 24, 1-17

Abstract: This study investigated the stability and bifurcation of a nonlinear system model developed by Marhl et al. based on the total Ca 2+ concentration among three different Ca 2+ stores. In this study, qualitative theories of center manifold and bifurcation were used to analyze the stability of equilibria. The bifurcation parameter drove the system to undergo two supercritical bifurcations. It was hypothesized that the appearance and disappearance of Ca 2+ oscillations are driven by them. At the same time, saddle-node bifurcation and torus bifurcation were also found in the process of exploring bifurcation. Finally, numerical simulation was carried out to determine the validity of the proposed approach by drawing bifurcation diagrams, time series, phase portraits, etc.

Keywords: bifurcation; chaos; hopf bifurcation; center manifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/24/3324/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/24/3324/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:24:p:3324-:d:706996

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().