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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 276059, 13 pages
Research Article

Fractional Dynamics in Calcium Oscillation Model

Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Chalongkrung Road, Ladkrabang, Bangkok 10520, Thailand

Received 20 April 2014; Revised 8 June 2014; Accepted 1 July 2014

Academic Editor: Shaofan Li

Copyright © 2015 Yoothana Suansook and Kitti Paithoonwattanakij. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The calcium oscillations have many important roles to perform many specific functions ranging from fertilization to cell death. The oscillation mechanisms have been observed in many cell types including cardiac cells, oocytes, and hepatocytes. There are many mathematical models proposed to describe the oscillatory changes of cytosolic calcium concentration in cytosol. Many experiments were observed in various kinds of living cells. Most of the experimental data show simple periodic oscillations. In certain type of cell, there exists the complex periodic bursting behavior. In this paper, we have studied further the fractional chaotic behavior in calcium oscillations model based on experimental study of hepatocytes proposed by Kummer et al. Our aim is to explore fractional-order chaotic pattern in this oscillation model. Numerical calculation of bifurcation parameters is carried out using modified trapezoidal rule for fractional integral. Fractional-order phase space and time series at fractional order are present. Numerical results are characterizing the dynamical behavior at different fractional order. Chaotic behavior of the model can be analyzed from the bifurcation pattern.