Fractal Dimension Analysis of the Julia Sets of Controlled Brusselator Model by Yuqian Deng, Xiuxiong Liu, Yongping Zhang

“…In this paper, the Julia set of Brusselator model which is a class of reaction diffusion equations from the viewpoint of fractal dynamics is discussed, and the control of the Julia set is researched by feedback control method, optimal control method, and gradient control method, respectively. …”
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Optimal network sizes for most robust Turing patterns by Hazlam S. Ahmad Shaberi, Aibek Kappassov, Antonio Matas-Gil, Robert G. Endres

“…Abstract Many cellular patterns exhibit a reaction-diffusion component, suggesting that Turing instability may contribute to pattern formation. …”
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Pattern formation of a predator-prey model with the cost of anti-predator behaviors by Xiaoying Wang, Xingfu Zou

“…We propose and analyse a reaction-diffusion-advection predator-prey model in which we assume that predators move randomly but prey avoid predation by perceiving a repulsion along predator density gradient. …”
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An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher–Kolmogorov–Petrovsky–Piskunov Equation by Sangkwon Kim, Chaeyoung Lee, Hyun Geun Lee, Hyundong Kim, Soobin Kwak, Youngjin Hwang, Seungyoon Kang, Seokjun Ham, Junseok Kim

“…The Fisher–KPP equation is a reaction-diffusion system that can be used to model population growth and wave propagation. …”
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Protocomputing Architecture over a Digital Medium Aiming at Real-Time Video Processing by Aoi Tanibata, Alexandre Schmid, Shinya Takamaeda-Yamazaki, Masayuki Ikebe, Masato Motomura, Tetsuya Asai

“…A protocomputational architecture is presented that implements the ancient reaction-diffusion model as a microelectronic hardware. …”
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The velocity diagram for traveling waves by Al Haj, Mohammad, Monneau, Régis

“…In this Note, we consider traveling waves in a reaction-diffusion equation in dimension one. Motivated by the motion of dislocations in crystals, we introduce an additive parameter $\sigma $ in the reaction term, which may be interpreted as an exterior force applied on the crystal. …”
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Fairy circles and temporal periodic patterns in the delayed plant-sulfide feedback model by Xin Wei, Jianjun Paul Tian, Jiantao Zhao

“…Incorporating the self-regulatory mechanism with time delay to a plant-sulfide feedback system for intertidal salt marshes, we proposed and studied a functional reaction-diffusion model. We analyzed the stability of the positive steady state of the system, and derived the sufficient conditions for the occurrence of Hopf bifurcations. …”
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The Effects of Mixing, Reaction Rates, and Stoichiometry on Yield for Mixing Sensitive Reactions—Part I: Model Development by Syed Imran A. Shah, Larry W. Kostiuk, Suzanne M. Kresta

“…To investigate this, a 1D, dimensionless, reaction-diffusion model at the micromixing scale was developed. …”
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On the mathematical modelling of tumor-induced angiogenesis by Luis L. Bonilla, Vincenzo Capasso, Mariano Alvaro, Manuel Carretero, Filippo Terragni

“…On the other hand we have shown that ensemble averages over many realizations of the stochastic system may better correspond to a deterministic reaction-diffusion system.…”
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Spatial spread of sexually transmitted diseases within susceptible populations at demographic steady state by Carlos Castillo-Chavez, Bingtuan Li

“…In prior models, thesetransmission dynamics have only been studied in the context ofnonexplicitly mobile heterosexually active populations at thedemographic steady state, or, explicitly in the simplest contextof SIS frameworks whose limiting systems are order preserving.We introduce reaction-diffusion equations to study the dynamics ofsexually-transmitted diseases (STDs) in spatially mobileheterosexually active populations. …”
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A multiple time-scale computational model of a tumor and its micro environment by Christopher DuBois, Jesse Farnham, Eric Aaron, Ami Radunskaya

“…This paper describes anefficient, flexible, hybrid cellular automaton-based implementation ofnumerical solutions to multiple time-scale reaction-diffusion equations,applied to a model of tumor proliferation. …”
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The implications of model formulation when transitioning from spatial to landscape ecology by Robert Stephen Cantrell, Chris Cosner, William F. Fagan

“…In particular, we are interested in seeing how precisely the predictions of mathematically rich spatially explicit regimes (reaction-diffusion models, integro-difference models) can be matched by those of ostensibly mathematically simpler spatially implicit patch approximations (discrete-diffusion models, average dispersal success matrix models).…”
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A cell structure implementation of the multigrid method for the two-dimensional diffusion equation by Yongho Choi, Youngjin Hwang, Soobin Kwak, Seokjun Ham, Jyoti, Hyundong Kim, Junseok Kim

“…Some examples include the reaction–diffusion equations, the convection–diffusion equations, and others. …”
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Application of the Natural Decomposition Method to Strongly Coupled Partial Differential Equations: The Gray-Scott Model. by Nsingwire, Godwin

“…This study investigated the application of the natural decomposition method for solving the Gray-Scott reaction-diffusion model, which is known for its complex nonlinearities and strong coupling between chemical species. …”
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Pattern analysis in a benthic bacteria-nutrient system by Daniel Wetzel

“…We study steady states in a reaction-diffusion system for a benthic bacteria-nutrient model in a marine sediment over 1D and 2D domains by using Landau reductions and numerical path following methods. …”
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A spatial model of tumor-host interaction: Application of chemotherapy by Peter Hinow, Philip Gerlee, Lisa J. McCawley, Vito Quaranta, Madalina Ciobanu, Shizhen Wang, Jason M. Graham, Bruce P. Ayati, Jonathan Claridge, Kristin R. Swanson, Mary Loveless, Alexander R. A. Anderson

“…The model, which is of reaction-diffusion type, takes into account the complex interactions between the tumor and surrounding stromal cells by including densities of endothelial cells and the extra-cellular matrix. …”
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A mechanistic-statistical approach to infer dispersal and demography from invasion dynamics, applied to a plant pathogen by Saubin, Méline, Coville, Jérome, Xhaard, Constance, Frey, Pascal, Soubeyrand, Samuel, Halkett, Fabien, Fabre, Frédéric

“…The mechanistic model takes into account population growth and grasps the diversity in dispersal processes by using either diffusion, leading to a reaction-diffusion (R.D.) formalism, or kernels, leading to an integro-differential (I.D.) formalism. …”
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Lattice defect engineering advances n-type PbSe thermoelectrics by Qian Deng, Xiao-Lei Shi, Meng Li, Xiaobo Tan, Ruiheng Li, Chen Wang, Yue Chen, Hongliang Dong, Ran Ang, Zhi-Gang Chen

“…Moreover, a robust Co/PbSe interface is designed to effectively prevent chemical reactions/diffusion; this interface exhibited a low electrical contact resistivity of ~10.9 μΩ cm2, excellent durability, and good stability in the thermoelectric module, which achieves a record-high conversion efficiency of 13.1% at a temperature difference of 460 K in segmented thermoelectric modules. …”
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