Numerical simulations of chaotic and complex spatiotemporal patterns in fractional reaction–diffusion systems

2017 ◽  
Vol 37 (2) ◽  
pp. 2166-2189 ◽  
Author(s):  
Kolade M. Owolabi ◽  
Abdon Atangana
Keyword(s):  
Numerical Simulations ◽  
Reaction Diffusion ◽  
Spatiotemporal Patterns ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Fractional Reaction

scholarly journals A Nonlocal Eigenvalue Problem and the Stability of Spikes for Reaction–Diffusion Systems with Fractional Reaction Rates

2003 ◽  
Vol 13 (06) ◽  
pp. 1529-1543 ◽  
Author(s):  
Juncheng Wei ◽  
Matthias Winter
Keyword(s):  
Eigenvalue Problem ◽  
Reaction Diffusion ◽  
Reaction Rates ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
The Stability ◽  
Nonlocal Eigenvalue Problem ◽  
Fractional Reaction

We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction–diffusion systems with fractional reaction rates such as the Sel'kov model, the Gray–Scott system, the hypercycle of Eigen and Schuster, angiogenesis, and the generalized Gierer–Meinhardt system. We give some sufficient and explicit conditions for stability by studying the corresponding nonlocal eigenvalue problem in a new range of parameters.

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