Abstract
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.
Highlights
The behaviors of many physical systems are nonlinear
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
The Poincare-Bendixson theorem states that continuous dynamical systems cannot exhibit chaotic attractor if dimension is less than three
Summary
The behaviors of many physical systems are nonlinear. The study of complexity arising from nonlinear systems is an intrigue subject for scientific research. Nonlinear dynamical systems have many interesting behaviors to study The research in this field starts from the discovery of chaos in atmospheric convection model by Lorenz [1]. The equations that described the dynamical system are differential equations which yield different type of solutions [2] such as limit cycle, periodic, periodic doubling, nonperiodic, and chaotic solutions Further studies in this field are chaos synchronization [3] and fractional-order dynamical system [4,5,6,7,8,9,10,11,12,13,14,15,16,17]
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