Existence and global asymptotic stability in a fractional double parabolic chemotaxis system with logistic source

2022 ◽  
Vol 217 ◽  
pp. 112750
Author(s):  
Yuzhu Lei ◽  
Zuhan Liu ◽  
Ling Zhou
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Logistic Source ◽  
Chemotaxis System

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.

scholarly journals On Global Asymptotic Stability for the LSW Model with Subcritical Initial Data

2019 ◽  
Vol 178 (1) ◽  
pp. 117-177
Author(s):  
Joseph G. Conlon ◽  
Michael Dabkowski
Keyword(s):  
Asymptotic Stability ◽  
Initial Data ◽  
Global Asymptotic Stability
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