Stochastic dynamics in the Li–Rinzel calcium oscillation model

2021 ◽  
Author(s):  
Lev Ryashko ◽  
Irina Bashkirtseva ◽  
Olga Solovyova
Keyword(s):  
Stochastic Dynamics ◽  
Calcium Oscillation ◽  
Oscillation Model

scholarly journals Different Types of Periodic Activities in a Calcium Oscillation Model

2013 ◽  
Vol 7 (6) ◽  
pp. 2515-2518
Author(s):  
Li Yuanhua ◽  
Zhouand Yi ◽  
Ji Quanbao
Keyword(s):  
Calcium Oscillation ◽  
Oscillation Model ◽  
Different Types

scholarly journals Fractional Dynamics in Calcium Oscillation Model

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yoothana Suansook ◽  
Kitti Paithoonwattanakij
Keyword(s):  
Fractional Order ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Cell Types ◽  
Cytosolic Calcium ◽  
Cardiac Cells ◽  
Calcium Oscillations ◽  
Calcium Oscillation ◽  
Fractional Dynamics ◽  
Oscillation Model

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.

HOPF BIFURCATION IN A CALCIUM OSCILLATION MODEL AND ITS CONTROL: FREQUENCY DOMAIN APPROACH

2013 ◽  
Vol 23 (01) ◽  
pp. 1350012 ◽  
Author(s):  
YU CHANG ◽  
LILI ZHOU ◽  
JINLIANG WANG
Keyword(s):  
Hopf Bifurcation ◽  
Frequency Domain ◽  
Periodic Orbits ◽  
Harmonic Balance ◽  
Bifurcation Theory ◽  
Harmonic Balance Method ◽  
Calcium Oscillation ◽  
Control Frequency ◽  
Oscillation Model ◽  
Frequency Domain Approach

The Hopf bifurcation in a calcium oscillation model is theoretically analyzed by Hopf bifurcation theory in frequency domain. Approximation expressions for frequencies and amplitudes of periodic orbits arising from Hopf bifurcation are provided by using second-order harmonic balance method. In addition, a new method is proposed to control the amplitudes of the periodic orbits. Numerical simulations show the effectiveness of the method for suppressing periodic oscillations.

Chaos in a calcium oscillation model via Atangana-Baleanu operator with strong memory

2019 ◽  
Vol 134 (4) ◽  
Author(s):  
J. F. Gómez-Aguilar ◽  
Kashif Ali Abro ◽  
Olusola Kolebaje ◽  
Ahmet Yildirim
Keyword(s):  
Calcium Oscillation ◽  
Oscillation Model
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