scholarly journals Wavefronts for a global reaction–diffusion population model with infinite distributed delay

2008 ◽  
Vol 345 (1) ◽  
pp. 522-534 ◽  
Author(s):  
Peixuan Weng ◽  
Zhiting Xu
Keyword(s):  
Population Model ◽  
Distributed Delay ◽  
Reaction Diffusion ◽  
Global Reaction

scholarly journals A hunter-gatherer–farmer population model: Lie symmetries, exact solutions and their interpretation

2018 ◽  
Vol 30 (2) ◽  
pp. 338-357 ◽  
Author(s):  
R. M. CHERNIHA ◽  
V. V. DAVYDOVYCH
Keyword(s):  
Exact Solutions ◽  
Population Model ◽  
Reaction Diffusion ◽  
Lie Symmetry ◽  
Lie Symmetries ◽  
System Modelling ◽  
Hunter Gatherers ◽  
Three Component Reaction ◽  
Biological Interpretation

The Lie symmetry classification of the known three-component reaction–diffusion system modelling the spread of an initially localized population of farmers into a region occupied by hunter-gatherers is derived. The Lie symmetries obtained for reducing the system in question to systems of ordinary differential equations (ODEs) and constructing exact solutions are applied. Several exact solutions of travelling front type are also found, their properties are identified and biological interpretation is discussed.

Study of an A+2B--->C Reaction-Diffusion System with Initially Separated Components

1994 ◽  
Vol 366 ◽  
Author(s):  
Andrew Yen ◽  
Raoul Kopelman
Keyword(s):  
Reaction Front ◽  
Reaction Rate ◽  
Reaction Diffusion ◽  
Biological Processes ◽  
Local Production ◽  
Kinetic Behavior ◽  
Acetate Trihydrate ◽  
Physical Chemical ◽  
Global Reaction ◽  
Front Dynamics

ABSTRACTThe presence of a reaction front is a characteristic feature of a variety of physical, chemical and biological processes. A chemical reaction exhibits a front (spatially localized region where concentration of product is non zero), provided the diffusing reactants are separated in space. We study the reaction front dynamics of a termolecular A+2B--->C reaction with initially separated components in a capillary. The reaction tetra+2Ni2+--->1:2 complex is used, where ‘tetra’ is disodium ethyl bis(5-tetrazolylazo) acetate trihydrate. We measure and compare with theory the dynamic quantities that characterize the kinetic behavior of the system: the global reaction rate R(t), the location of the reaction center xf(t), the front's width w(t), and the local production rate R(xf,t). The non-classical nature of this dynamical system is confirmed.

scholarly journals Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Ruofeng Rao ◽  
Shouming Zhong
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Distributed Delay ◽  
Reaction Diffusion ◽  
Cellular Neural Network ◽  
Point Theory ◽  
Complete Space ◽  
Practical Engineering ◽  
The Fixed Point Theorem ◽  
The Stability

This paper investigates the stochastically exponential stability of reaction-diffusion impulsive stochastic cellular neural networks (CNN). The reaction-diffusion pulse stochastic system model characterizes the complexity of practical engineering and brings about mathematical difficulties, too. However, the difficulties have been overcome by constructing a new contraction mapping and an appropriate distance on a product space which is guaranteed to be a complete space. This is the first time to employ the fixed point theorem to derive the stability criterion of reaction-diffusion impulsive stochastic CNN with distributed time delays. Finally, an example is provided to illustrate the effectiveness of the proposed methods.

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