scholarly journals Asymptotic synchronization of fractional order non-identical complex dynamical networks with Parameter Uncertainties

2021 ◽  
Author(s):  
S Aadhithiyan ◽  
R. Raja ◽  
Bo Kou ◽  
G Selvam ◽  
Michal Niezabitowski ◽  
...  
Keyword(s):  
Complex Networks ◽  
Fractional Order ◽  
Lyapunov Method ◽  
Direct Lyapunov Method ◽  
Parameter Uncertainties ◽  
Complex Dynamic ◽  
Fractional Order Calculus ◽  
Response System ◽  
Liouville Derivative ◽  
Asymptotic Synchronization

This article specically deals with the asymptotic synchronization of non-identical complex dynamic fractional order networks with uncertainty. Initially, by using the Riemann-Liouville derivative, we developed a model for the general non-identical complex network, and based on the properties of fractional order calculus and the direct Lyapunov method in fractional order, we proposed that drive and response system if nonidentical complex networks ensuring asymp-totic synchronization by using neoteric control. Second, taking into account the uncertainties of non-identical complex networks in state matrices and evaluating theirrequirements forasymptotic synchronization. In addition, to explain the eectiveness of the proposed approach, two numerical simulations are given.

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

Global stability analysis of fractional-order gene regulatory networks with time delay

2019 ◽  
Vol 12 (06) ◽  
pp. 1950067 ◽  
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Existence And Uniqueness ◽  
Regulatory Networks ◽  
Lyapunov Method ◽  
Regulation Mechanism ◽  
Global Stability Analysis ◽  
Gene Regulatory ◽  
The Stability

Fractional-order gene regulatory networks with time delay (DFGRNs) have proven that they are more suitable to model gene regulation mechanism than integer-order. In this paper, a novel DFGRN is proposed. The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions. On this basis, the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN, and the stability conditions are dependent on the fractional-order [Formula: see text]. Finally, numerical simulations show that the obtained results are reasonable.

Predicting the aggressiveness of peripheral zone prostate cancer using a fractional order calculus diffusion model

2021 ◽  
Vol 143 ◽  
pp. 109913
Author(s):  
Zhihua Li ◽  
Guangyu Dan ◽  
Vikram Tammana ◽  
Scott Johnson ◽  
Zheng Zhong ◽  
...  
Keyword(s):  
Prostate Cancer ◽  
Diffusion Model ◽  
Fractional Order ◽  
Peripheral Zone ◽  
Fractional Order Calculus

scholarly journals Studies of anomalous diffusion in the human brain using fractional order calculus

2010 ◽  
Vol 63 (3) ◽  
pp. 562-569 ◽  
Author(s):  
Xiaohong Joe Zhou ◽  
Qing Gao ◽  
Osama Abdullah ◽  
Richard L. Magin
Keyword(s):  
Human Brain ◽  
Fractional Order ◽  
Anomalous Diffusion ◽  
Fractional Order Calculus

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document