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.

Complex Dynamics in the Kummer-Olsen Model of Calcium Oscillations

2012 ◽  
Vol 226-228 ◽  
pp. 505-509
Author(s):  
Zheng Fei Wu ◽  
Yi Zhou
Keyword(s):  
Theoretical Analysis ◽  
Calcium Release ◽  
Complex Dynamics ◽  
Cytosolic Calcium ◽  
Vital Role ◽  
Calcium Oscillations ◽  
Calcium Oscillation ◽  
Center Manifold Theorem ◽  
Oscillation Model ◽  
Calcium Induced Calcium Release

Oscillations of cytosolic calcium concentration, known as calcium oscillations, play a vital role in providing the intracellular signalling. These oscillations are explained with a model based on calcium-induced calcium release (CICR). The nonlinear dynamics of the Kummer-Olsen calcium oscillation model is discussed by using the center manifold theorem and bifurcation theory, including the variation in classification and stability of equilibria with parameter value. It is concluded that the appearance and disappearance of calcium oscillations in this system is due to supercritical Hopf bifurcation of equilibria. Finally, numerical simulations are carried out to support the theoretical analysis of the research. By combining the existing numerical results with the theoretical analysis results in this paper, a complete description of the dynamics of the Kummer-Olsen calcium oscillation model has now been obtained.

scholarly journals On an Optimal Control Applied in MEMS Oscillator with Chaotic Behavior including Fractional Order

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Angelo Marcelo Tusset ◽  
Frederic Conrad Janzen ◽  
Rodrigo Tumolin Rocha ◽  
Jose Manoel Balthazar
Keyword(s):  
Fractional Order ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Dynamical Analysis ◽  
Linear Feedback ◽  
Nonlinear Stiffness ◽  
Mems Resonator ◽  
Optimal Linear ◽  
Mems Oscillator ◽  
Resonator System

The dynamical analysis and control of a nonlinear MEMS resonator system is considered. Phase diagram, power spectral density (FFT), bifurcation diagram, and the 0-1 test were applied to analyze the influence of the nonlinear stiffness term related to the dynamics of the system. In addition, the dynamical behavior of the system is considered in fractional order. Numerical results showed that the nonlinear stiffness parameter and the order of the fractional order were significant, indicating that the response can be either a chaotic or periodic behavior. In order to bring the system from a chaotic state to a periodic orbit, the optimal linear feedback control (OLFC) is considered. The robustness of the proposed control is tested by a sensitivity analysis to parametric uncertainties.

scholarly journals Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 165
Author(s):  
Zai-Yin He ◽  
Abderrahmane Abbes ◽  
Hadi Jahanshahi ◽  
Naif D. Alotaibi ◽  
Ye Wang
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Epidemic Model ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Maximum Lyapunov Exponent ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Reasonable Range ◽  
Fractional Orders

This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors, bifurcation diagrams, maximum Lyapunov exponent and the 0−1 test, it is verified that the newly introduced fractional discrete SIR epidemic model vaccination with both commensurate and incommensurate fractional orders has chaotic behavior. The discrete fractional model gives more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders. The reasonable range of commensurate fractional orders is between γ = 0.8712 and γ = 1, while the reasonable range of incommensurate fractional orders is between γ2 = 0.77 and γ2 = 1. Furthermore, the complexity analysis is performed using approximate entropy (ApEn) and C0 complexity to confirm the existence of chaos. Finally, simulations were carried out on MATLAB to verify the efficacy of the given findings.

scholarly journals Dual Mode of Action of Acetylcholine on Cytosolic Calcium Oscillations in Pancreatic Beta and Acinar Cells In Situ

Cells ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 1580
Author(s):  
Nastja Sluga ◽  
Sandra Postić ◽  
Srdjan Sarikas ◽  
Ya-Chi Huang ◽  
Andraž Stožer ◽  
...  
Keyword(s):  
Beta Cells ◽  
Acinar Cells ◽  
Cell Types ◽  
Cytosolic Calcium ◽  
Calcium Oscillations ◽  
The Body ◽  
Cholinergic Innervation ◽  
Oscillatory Activity ◽  
Tissue Slices

Cholinergic innervation in the pancreas controls both the release of digestive enzymes to support the intestinal digestion and absorption, as well as insulin release to promote nutrient use in the cells of the body. The effects of muscarinic receptor stimulation are described in detail for endocrine beta cells and exocrine acinar cells separately. Here we describe morphological and functional criteria to separate these two cell types in situ in tissue slices and simultaneously measure their response to ACh stimulation on cytosolic Ca2+ oscillations [Ca2+]c in stimulatory glucose conditions. Our results show that both cell types respond to glucose directly in the concentration range compatible with the glucose transporters they express. The physiological ACh concentration increases the frequency of glucose stimulated [Ca2+]c oscillations in both cell types and synchronizes [Ca2+]c oscillations in acinar cells. The supraphysiological ACh concentration further increases the oscillation frequency on the level of individual beta cells, inhibits the synchronization between these cells, and abolishes oscillatory activity in acinar cells. We discuss possible mechanisms leading to the observed phenomena.

scholarly journals Independently paced calcium oscillations in progenitor and differentiated cells in an ex vivo epithelial organ

2021 ◽  
Author(s):  
Anna Kim ◽  
Amanda Nguyen ◽  
Marco Marchetti ◽  
Denise Montell ◽  
Beth Pruitt ◽  
...  
Keyword(s):  
Stem Cells ◽  
Ex Vivo ◽  
Cell Types ◽  
Cytosolic Calcium ◽  
Calcium Oscillations ◽  
Enteroendocrine Cells ◽  
Calcium Dynamics ◽  
Differentiated Cells ◽  
Different Cell Types

Cytosolic calcium is a highly dynamic, tightly regulated, and broadly conserved cellular signal. Calcium dynamics have been studied widely in cellular monocultures, yet in vivo most organs comprise heterogeneous populations of stem and differentiated cells. We examined calcium dynamics in each cell type of the adult Drosophila intestine, a self-renewing epithelial organ where multipotent stem cells give rise to mature absorptive enterocytes and secretory enteroendocrine cells. Here we perform live imaging of whole organs ex vivo, and we employ orthogonal expression of red and green calcium sensors to determine whether calcium oscillations between different cell types are coupled. We show that stem cell daughters adopt strikingly distinct patterns of calcium oscillations when they acquire their terminal fates: enteroendocrine cells exhibit single-cell calcium oscillations, while long-range calcium waves propagate rhythmically across large fields of enterocytes. These multicellular waves do not propagate through progenitor cells (stem cells and undifferentiated enterocyte precursors), whose oscillation frequency is approximately half that of enteroendocrine cells. Organ-scale inhibition of gap junctions eliminates calcium oscillations in all three cell types, even, intriguingly, in progenitor and enteroendocrine cells that are surrounded only by enterocytes. Our findings establish that cells adopt fate-specific modes of calcium dynamics as they terminally differentiate and reveal that the oscillatory dynamics of different cell types in the same epithelium are paced independently.

scholarly journals A Discrete Fractional-Order Prion Model Motivated by Parkinson’s Disease

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
M. F. Elettreby ◽  
E. Ahmed ◽  
A. S. Alqahtani
Keyword(s):  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Fractional Order ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Disease Model ◽  
Equation Model ◽  
Wide Range ◽  
The Stability ◽  
Uniqueness Of A Solution

A prion differential equation model motivated by Parkinson’s disease (PD) is studied. A fractional-order form of this model is proposed. After that, we discretized fractional-order Parkinson’s disease model. A sufficient condition for the existence and the uniqueness of a solution to the system is obtained. The stability of the fixed points of the system is achieved by using the Jury test. The impacts of varying the parameters of the system are examined. Under certain conditions, the system undergoes some kinds of bifurcations. We observe that the model loses its stability through double-period bifurcation to chaotic behavior as the growth rate increases. Also, the system stabilizes by increasing the memory parameter, and the contact rate between the two types of prions increases. The system shows rich dynamical behavior for a wide range of the values of the parameters.

scholarly journals Maximizing the Chaotic Behavior of Fractional Order Chen System by Evolutionary Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1194
Author(s):  
Jose-Cruz Nuñez-Perez ◽  
Vincent-Ademola Adeyemi ◽  
Yuma Sandoval-Ibarra ◽  
Francisco-Javier Perez-Pinal ◽  
Esteban Tlelo-Cuautle
Keyword(s):  
Evolutionary Algorithms ◽  
Fractional Order ◽  
Chaotic Behavior ◽  
Optimization Algorithms ◽  
Dynamical Behavior ◽  
Optimization Techniques ◽  
Maximum Lyapunov Exponent ◽  
Invasive Weed Optimization ◽  
Chen System ◽  
Invasive Weed

This paper presents the application of three optimization algorithms to increase the chaotic behavior of the fractional order chaotic Chen system. This is achieved by optimizing the maximum Lyapunov exponent (MLE). The applied optimization techniques are evolutionary algorithms (EAs), namely: differential evolution (DE), particle swarm optimization (PSO), and invasive weed optimization (IWO). In each algorithm, the optimization process is performed using 100 individuals and generations from 50 to 500, with a step of 50, which makes a total of ten independent runs. The results show that the optimized fractional order chaotic Chen systems have higher maximum Lyapunov exponents than the non-optimized system, with the DE giving the highest MLE. Additionally, the results indicate that the chaotic behavior of the fractional order Chen system is multifaceted with respect to the parameter and fractional order values. The dynamical behavior and complexity of the optimized systems are verified using properties, such as bifurcation, LE spectrum, equilibrium point, eigenvalue, and sample entropy. Moreover, the optimized systems are compared with a hyper-chaotic Chen system on the basis of their prediction times. The results show that the optimized systems have a shorter prediction time than the hyper-chaotic system. The optimized results are suitable for developing a secure communication system and a random number generator. Finally, the Halstead parameters measure the complexity of the three optimization algorithms that were implemented in MATLAB. The results reveal that the invasive weed optimization has the simplest implementation.

scholarly journals Dual Mode of Action of Acetylcholine on Cytosolic Calcium Oscillations in Pancreatic Beta and Acinar Cells in Situ

2021 ◽  
Author(s):  
Nastja Sluga ◽  
Sandra Postic ◽  
Srdjan Sarikas ◽  
Ya-Chi Huang ◽  
Andraz Stožer ◽  
...  
Keyword(s):  
Beta Cells ◽  
Acinar Cells ◽  
Cell Types ◽  
Cytosolic Calcium ◽  
Calcium Oscillations ◽  
The Body ◽  
Cholinergic Innervation ◽  
Oscillatory Activity ◽  
Tissue Slices

Cholinergic innervation in pancreas controls both the release of digestive enzymes to support the intestinal digestion and absorption, as well as insulin release to promote nutrient use in the cells of the body. The effects of muscarinic receptor stimulation are described in detail for endocrine beta cells and exocrine acinar cells separately. Here we describe morphological and functional criteria to separate these two cell types in situ in tissue slices and simultaneously measure their response to ACh stimulation on cytosolic Ca2+ oscillations [Ca2+]c in stimulatory glucose conditions. Our results show that both cell types respond to glucose directly in the concentration range compatible with the glucose transporters they express. The physiological ACh concentration increases the frequency of glucose stimulated [Ca2+]c oscillations in both cell types and synchronizes [Ca2+]c oscillations in acinar cells. The pharmacological ACh concentration further increases the oscillation frequency on the level of individual beta cells, inhibits the synchronization between these cells, and abolishes oscillatory activity in acinar cells. We discuss possible mechanisms leading to the observed phenomena.

scholarly journals Dynamical analysis and adaptive fuzzy control for the fractional-order financial risk chaotic system

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sukono ◽  
Aceng Sambas ◽  
Shaobo He ◽  
Heng Liu ◽  
Sundarapandian Vaidyanathan ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Fuzzy Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Financial Risk ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Adaptive Fuzzy Control ◽  
Dynamical Analysis ◽  
Adaptive Fuzzy

AbstractIn this paper, a fractional-order model of a financial risk dynamical system is proposed and the complex behavior of such a system is presented. The basic dynamical behavior of this financial risk dynamic system, such as chaotic attractor, Lyapunov exponents, and bifurcation analysis, is investigated. We find that numerical results display periodic behavior and chaotic behavior of the system. The results of theoretical models and numerical simulation are helpful for better understanding of other similar nonlinear financial risk dynamic systems. Furthermore, the adaptive fuzzy control for the fractional-order financial risk chaotic system is investigated on the fractional Lyapunov stability criterion. Finally, numerical simulation is given to confirm the effectiveness of the proposed method.

CHAOTIC BEHAVIOR IN A FRACTIONAL-ORDER SYSTEM CONTAINING A CONTINUOUS ORDER-DISTRIBUTION

2012 ◽  
Vol 22 (10) ◽  
pp. 1250253 ◽  
Author(s):  
TOM T. HARTLEY ◽  
CARL F. LORENZO
Keyword(s):  
Nonlinear System ◽  
Fractional Order ◽  
Function Method ◽  
Chaotic Behavior ◽  
Order System ◽  
Fractional Dynamics ◽  
Approximation Methods ◽  
Describing Function ◽  
Describing Function Method ◽  
Bifurcation Behavior

This paper discusses the fractional dynamics, and the bifurcation behavior, of a specific nonlinear system that contains a continuous order-distribution. The dynamics of the system are predicted using the describing-function method. General approximation methods are then derived for the continuous order-distribution component. The system is simulated using these approximations, and the results compared with the describing-function predictions. This is believed to be the first observation of chaos in a system with continuous order-distribution.

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