Numerical simulations of Turing patterns in a reaction-diffusion model with the Chebyshev spectral method

2018 ◽  
Vol 133 (10) ◽  
Author(s):  
Maliha Tehseen Saleem ◽  
Ishtiaq Ali
Keyword(s):  
Numerical Simulations ◽  
Spectral Method ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Turing Patterns ◽  
Reaction Diffusion Model ◽  
Chebyshev Spectral Method

scholarly journals Hopf Bifurcation in an Oscillatory-Excitable Reaction–Diffusion Model with Spatial Heterogeneity

2017 ◽  
Vol 27 (05) ◽  
pp. 1750065
Author(s):  
Benjamin Ambrosio
Keyword(s):  
Hopf Bifurcation ◽  
Qualitative Analysis ◽  
Spatial Heterogeneity ◽  
Numerical Simulations ◽  
Diffusion Model ◽  
Center Manifold ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model

We focus on the qualitative analysis of a reaction–diffusion model with spatial heterogeneity. The system is a generalization of the well-known FitzHugh–Nagumo system, in which the excitability parameter is space dependent. This heterogeneity allows to exhibit concomitant stationary and oscillatory phenomena. We prove the existence of a Hopf bifurcation and determine an equation of the center-manifold in which the solution asymptotically evolves. Numerical simulations illustrate the phenomenon.

Stable Squares and Other Oscillatory Turing Patterns in a Reaction-Diffusion Model

2004 ◽  
Vol 92 (19) ◽  
Author(s):  
Lingfa Yang ◽  
Anatol M. Zhabotinsky ◽  
Irving R. Epstein
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Turing Patterns ◽  
Reaction Diffusion Model

scholarly journals Dynamic analysis of a malaria reaction-diffusion model with periodic delays and vector bias

2022 ◽  
Vol 19 (3) ◽  
pp. 2538-2574
Author(s):  
Hongyong Zhao ◽  
◽  
Yangyang Shi ◽  
Xuebing Zhang ◽  
◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Diffusion Model ◽  
Disease Transmission ◽  
Reaction Diffusion ◽  
Major Effect ◽  
Threshold Dynamics ◽  
Seasonal Temperature ◽  
Reaction Diffusion Model ◽  
Maturity Period ◽  
Globally Attractive

<abstract><p>One of the most important vector-borne disease in humans is malaria, caused by <italic>Plasmodium</italic> parasite. Seasonal temperature elements have a major effect on the life development of mosquitoes and the development of parasites. In this paper, we establish and analyze a reaction-diffusion model, which includes seasonality, vector-bias, temperature-dependent extrinsic incubation period (EIP) and maturation delay in mosquitoes. In order to get the model threshold dynamics, a threshold parameter, the basic reproduction number $ R_{0} $ is introduced, which is the spectral radius of the next generation operator. Quantitative analysis indicates that when $ R_{0} &lt; 1 $, there is a globally attractive disease-free $ \omega $-periodic solution; disease is uniformly persistent in humans and mosquitoes if $ R_{0} &gt; 1 $. Numerical simulations verify the results of the theoretical analysis and discuss the effects of diffusion and seasonality. We study the relationship between the parameters in the model and $ R_{0} $. More importantly, how to allocate medical resources to reduce the spread of disease is explored through numerical simulations. Last but not least, we discover that when studying malaria transmission, ignoring vector-bias or assuming that the maturity period is not affected by temperature, the risk of disease transmission will be underestimate.</p></abstract>

scholarly journals Turing patterns in a reaction–diffusion model with the Degn–Harrison reaction scheme

2015 ◽  
Vol 259 (5) ◽  
pp. 1990-2029 ◽  
Author(s):  
Shanbing Li ◽  
Jianhua Wu ◽  
Yaying Dong
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Scheme ◽  
Turing Patterns ◽  
Reaction Diffusion Model

Analysis and Numerical Simulations of a Reaction-Diffusion Model with Fixed Active Bodies

2021 ◽  
Vol 81 (4) ◽  
pp. 1339-1360
Author(s):  
Chang Yang ◽  
Léon Matar Tine
Keyword(s):  
Numerical Simulations ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model

scholarly journals A Semi-Automatic Numerical Algorithm for Turing Patterns Formation in a Reaction-Diffusion Model

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 4720-4724 ◽  
Author(s):  
Rosanna Campagna ◽  
Salvatore Cuomo ◽  
Francesco Giannino ◽  
Gerardo Severino ◽  
Gerardo Toraldo
Keyword(s):  
Diffusion Model ◽  
Numerical Algorithm ◽  
Reaction Diffusion ◽  
Turing Patterns ◽  
Reaction Diffusion Model
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