Global asymptotic stability for a class of discontinuous vector fields in

2007 ◽  
Vol 22 (2) ◽  
pp. 133-146 ◽  
Author(s):  
Jaume Llibre ◽  
Marco Antonio Teixeria
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Vector Fields ◽  
Discontinuous Vector Fields

scholarly journals Global asymptotic stability for differentiable vector fields of R2

2004 ◽  
Vol 206 (2) ◽  
pp. 470-482 ◽  
Author(s):  
Alexandre Fernandes ◽  
Carlos Gutierrez ◽  
Roland Rabanal
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Vector Fields ◽  
Differentiable Vector

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.

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