scholarly journals Dissipative Structures in a Nonlinear Reaction-Diffusion Model with Inhibition Forward: Global Nonuniform Steady Patterns, Spatio-Temporal Structures and Wave-Like Phenomena

1979 ◽  
Vol 61 (3) ◽  
pp. 801-814 ◽  
Author(s):  
V. Fairen ◽  
M. G. Velarde
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Dissipative Structures ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model ◽  
Temporal Structures ◽  
Spatio Temporal

scholarly journals Simulating Dengue: Comparison of Observed and Predicted Cases from Generic Reaction-Diffusion Model for Transmission of Mosquito-Borne Diseases

MATEMATIKA ◽  
2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Cynthia Mui Lian Kon ◽  
Jane Labadin
Keyword(s):  
Diffusion Model ◽  
Recovery Rate ◽  
Urban Areas ◽  
Reaction Diffusion ◽  
Severe Dengue ◽  
Generic Model ◽  
Reaction Diffusion Model ◽  
Temporal Model ◽  
Spatio Temporal ◽  
Actual Prevalence

Dengue is a mosquito-borne disease caused by virus and found mostly in urban and semi-urban areas, in many regions of the world. Female Aedes mosquitoes, which usually bite during daytime, spread the disease. This flu-like disease may progress to severe dengue and cause fatality. A generic reaction-diffusion model for transmission of mosquito-borne diseases was proposed and formulated. The motivation is to explore the ability of the generic model to reproduce observed dengue cases in Borneo, Malaysia. Dengue prevalence in four districts in Borneo namely Kuching, Sibu, Bintulu and Miri are compared with simulations results obtained from the temporal and spatio-temporal generic model respectively. Random diffusion of human and mosquito populations are taken into account in the spatio-temporal model. It is found that temporal simulations closely resemble the general behavior of actual prevalence in the three locations except for Bintulu. The recovery rate in Bintulu district is found to be the lowest among the districts, suggesting a different dengue serotype may be present. From observation, the temporal generic model underestimates the recovery rate in comparison to the spatio-temporal generic model.

scholarly journals Spatio-temporal Brusselator Model and Biological Pattern Formation

2021 ◽  
pp. 88-99
Author(s):  
Zakir Hossine ◽  
Oishi Khanam ◽  
Md. Mashih Ibn Yasin Adan ◽  
Md. Kamrujjaman
Keyword(s):  
Pattern Formation ◽  
Diffusion Model ◽  
Initial Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Brusselator Model ◽  
Reaction Diffusion Model ◽  
Biological Pattern Formation ◽  
Spatio Temporal

This paper explores a two-species non-homogeneous reaction-diffusion model for the study of pattern formation with the Brusselator model. We scrutinize the pattern formation with initial conditions and Neumann boundary conditions in a spatially heterogeneous environment. In the whole investigation, we assume the case for random diffusion strategy. The dynamics of model behaviors show that the nature of pattern formation with varying parameters and initial conditions thoroughly. The model also studies in the absence of diffusion terms. The theoretical and numerical observations explain pattern formation using the reaction-diffusion model in both one and two dimensions.

Notizen: Comparison Between a Generic Reaction- Diffusion Model and a Synergetic Semiconductor System

1987 ◽  
Vol 42 (6) ◽  
pp. 655-656
Author(s):  
J. Parisi ◽  
J. Peinke ◽  
B. Röhricht ◽  
U. Rau ◽  
M. Klein ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Diffusion Model ◽  
Physical Interpretation ◽  
Reaction Diffusion ◽  
Dynamical Model ◽  
Nonlinear Transport ◽  
Reaction Diffusion Model ◽  
Semiconductor System ◽  
Spatio Temporal ◽  
Simple Dynamical Model

This paper gives a concrete physical interpretation of a simple dynamical model based on the universal Rashevsky- Turing theory of symmetry-breaking morphogenesis in terms of spatio-temporal nonlinear transport phenomena in a synergetic semiconductor system.

Traveling wavefronts of a nonlinear reaction–diffusion model of tumor growth under the acid environment

2014 ◽  
Vol 07 (03) ◽  
pp. 1450034
Author(s):  
Huiyan Zhu ◽  
Yang Luo ◽  
Xiufang Wang
Keyword(s):  
Diffusion Model ◽  
Perturbation Methods ◽  
Tumor Tissue ◽  
Reaction Diffusion ◽  
Traveling Wave Solution ◽  
Ion Concentration ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Reaction ◽  
Reaction Diffusion Model ◽  
Acid Environment

In this paper, a reaction–diffusion model describing temporal development of tumor tissue, normal tissue and excess H+ ion concentration is considered. Based on a combination of perturbation methods, the Fredholm theory and Banach fixed point theorem, we theoretically justify the existence of the traveling wave solution for this model.

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