scholarly journals Heterogeneity and strong competition in ecology

2018 ◽  
Vol 30 (04) ◽  
pp. 682-706
Author(s):  
H. HUTRIDURGA ◽  
C. VENKATARAMAN
Keyword(s):  
Evolution Equation ◽  
Numerical Simulations ◽  
Diffusion Model ◽  
Limit Problem ◽  
Effective Coefficients ◽  
Spatial Dimensions ◽  
Strong Competition ◽  
Competition Diffusion

We study a competition-diffusion model while performing simultaneous homogenization and strong competition limits. The limit problem is shown to be a Stefan-type evolution equation with effective coefficients. We also perform some numerical simulations in one and two spatial dimensions that suggest that oscillations in motilities are detrimental to invasion behaviour of a species.

ON THE APPLICATION OF A NOVEL ALGORITHM TO HYDRODYNAMIC DIFFUSION AND VELOCITY FLUCTUATIONS IN SEDIMENTING SYSTEMS

1996 ◽  
Vol 07 (04) ◽  
pp. 543-561 ◽  
Author(s):  
WOLFGANG KALTHOFF ◽  
STEFAN SCHWARZER ◽  
GERALD RISTOW ◽  
HANS J. HERRMANN
Keyword(s):  
Numerical Simulations ◽  
Numerical Method ◽  
Incompressible Fluids ◽  
Strong Anisotropy ◽  
Velocity Fluctuations ◽  
Drag Forces ◽  
Large Numbers ◽  
Spatial Dimensions ◽  
Experimental Findings ◽  
Novel Algorithm

We present a numerical method to deal efficiently with large numbers of particles in incompressible fluids. The interactions between particles and fluid are taken into account by a physically motivated ansatz based on locally defined drag forces. We demonstrate the validity of our approach by performing numerical simulations of sedimenting non-Brownian spheres in two spatial dimensions and compare our results with experiments. Our method reproduces qualitatively important aspects of the experimental findings, in particular the strong anisotropy of the hydrodynamic bulk self-diffusivities.

scholarly journals Synchronization of the Glycolysis Reaction-Diffusion Model via Linear Control Law

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1516
Author(s):  
Adel Ouannas ◽  
Iqbal M. Batiha ◽  
Stelios Bekiros ◽  
Jinping Liu ◽  
Hadi Jahanshahi ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Linear Control ◽  
Control Law ◽  
Synchronization Problem ◽  
Reaction Diffusion Model ◽  
Spatial Dimensions ◽  
Error System ◽  
The Stability ◽  
Complex Formations

The Selkov system, which is typically employed to model glycolysis phenomena, unveils some rich dynamics and some other complex formations in biochemical reactions. In the present work, the synchronization problem of the glycolysis reaction-diffusion model is handled and examined. In addition, a novel convenient control law is designed in a linear form and, on the other hand, the stability of the associated error system is demonstrated through utilizing a suitable Lyapunov function. To illustrate the applicability of the proposed schemes, several numerical simulations are performed in one- and two-spatial dimensions.

Asymptotic behaviour, uniqueness and stability of coexistence states of a non-cooperative reaction–diffusion model of nuclear reactors

2010 ◽  
Vol 140 (1) ◽  
pp. 189-201 ◽  
Author(s):  
Rui Peng ◽  
Dong Wei ◽  
Guoying Yang
Keyword(s):  
Asymptotic Behaviour ◽  
Diffusion Model ◽  
Blow Up ◽  
Nuclear Reactors ◽  
Reaction Diffusion ◽  
Fast Neutrons ◽  
Fuel Temperature ◽  
Reaction Diffusion Model ◽  
Coexistence States ◽  
Spatial Dimensions

We investigate a non-cooperative reaction-diffusion model arising in the theory of nuclear reactors and are concerned with the associated steady-state problem. We determine the asymptotic behaviour of the coexistence states near the point of bifurcation from infinity, which exhibits the following very interesting spatial blow-up pattern: when the fuel temperature reaches a certain value, the free fast neutrons undergoing nuclear reaction will blow up in each spatial point of the interior of the reactor. Without any restriction on spatial dimensions, we also discuss the uniqueness and stability of the coexistence states. Our results complement and sharpen those derived in two recent works by Arioli and Lóopez-Gómez.

Affinity based information diffusion model in social networks

2014 ◽  
Vol 25 (05) ◽  
pp. 1440004 ◽  
Author(s):  
Hongli Liu ◽  
Yun Xie ◽  
Haibo Hu ◽  
Zhigao Chen
Keyword(s):  
Social Networks ◽  
Numerical Simulations ◽  
Diffusion Model ◽  
Information Diffusion ◽  
Propagation Speed ◽  
Average Degree ◽  
Information Propagation ◽  
Final Size ◽  
Information Diffusion Model ◽  
Intuitive Sense

There is a widespread intuitive sense that people prefer participating in spreading the information in which they are interested. The affinity of people with information disseminated can affect the information propagation in social networks. In this paper, we propose an information diffusion model incorporating the mechanism of affinity of people with information which considers the fitness of affinity values of people with affinity threshold of the information. We find that the final size of information diffusion is affected by affinity threshold of the information, average degree of the network and the probability of people's losing their interest in the information. We also explore the effects of other factors on information spreading by numerical simulations and find that the probabilities of people's questioning and confirming the information can affect the propagation speed, but not the final scope.

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.

scholarly journals Thin Film Limits in Magnetoelastic Interactions

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Mohammed Hadda ◽  
Mouhcine Tilioua
Keyword(s):  
Thin Film ◽  
Evolution Equation ◽  
Energy Method ◽  
Limit Problem ◽  
2D And 3D ◽  
Magnetization Field

This paper deals with classical dimensional reductions 3D-2D and 3D-1D in magnetoelastic interactions. We adopt a model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem both for flat and slender media by using the so-called energy method.

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