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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xinxin Qie & Quanbao Ji, 2021. "Computational Analysis and Bifurcation of Regular and Chaotic Ca 2+ Oscillations," Mathematics, MDPI, vol. 9(24), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3324-:d:706996
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