The resonance phenomenon in the reaction–diffusion systems by A. I. Lebanov, A. P. Chernyaev, T. K. Starozhilova

“…A new mechanism of pattern formation different from the Turing and oscillatory instabilities in the reaction–diffusion systems was found. It is closely connected with the resonance phenomenon that appears in the models when Jacobi's matrix of the kinetic part is equivalent to Jordan cell and diffusion coefficients are cited. …”
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Kinetics of quantum reaction-diffusion systems by Federico Gerbino, Igor Lesanovsky, Gabriele Perfetto

“…This open quantum dynamics represents a generalisation of classical reaction-diffusion dynamics to the quantum realm. We first show how initial conditions can be introduced in the Keldysh path integral via boundary terms. …”
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A Numerical Method for Time-Fractional Reaction-Diffusion and Integro Reaction-Diffusion Equation Based on Quasi-Wavelet by Sachin Kumar, Jinde Cao, Xiaodi Li

“…In this research work, we focused on finding the numerical solution of time-fractional reaction-diffusion and another class of integro-differential equation known as the integro reaction-diffusion equation. …”
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On the Speed of Spread for Fractional Reaction-Diffusion Equations by Hans Engler

“…The fractional reaction diffusion equation 𝜕𝑡𝑢+𝐴𝑢=𝑔(𝑢) is discussed, where 𝐴 is a fractional differential operator on ℝ of order 𝛼∈(0,2), the 𝐶1 function 𝑔 vanishes at 𝜁=0 and 𝜁=1, and either 𝑔≥0 on (0,1) or 𝑔<0 near 𝜁=0. …”
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Reaction-diffusion for fish populations with realistic mobility by Philip Broadbridge

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Regularity of Global Attractor for the Reaction-Diffusion Equation by Hong Luo

“…By using an iteration procedure, regularity estimates for the linear semigroups, and a classical existence theorem of global attractor, we prove that the reaction-diffusion equation possesses a global attractor in Sobolev space Hk for all k>0, which attracts any bounded subset of Hk(Ω) in the Hk-norm.…”
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Structure Preserving Numerical Analysis of Reaction-Diffusion Models by Nauman Ahmed, Muhammad Aziz-ur Rehman, Waleed Adel, Fahd Jarad, Mubasher Ali, Muhammad Rafiq, Ali Akgül

“…In this paper, we examine two structure preserving numerical finite difference methods for solving the various reaction-diffusion models in one dimension, appearing in chemistry and biology. …”
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Dynamics of an SIS reaction-diffusion epidemic model for diseasetransmission by Wenzhang Huang, Maoan Han, Kaiyu Liu

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Solving Reaction-Diffusion and Advection Problems with Richardson Extrapolation by Tamás Mona, István Lagzi, Ágnes Havasi

“…In this paper we investigate the efficiency of the Richardson method in one-dimensional numerical (reaction-diffusion) problems.…”
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Solving the Caputo Fractional Reaction-Diffusion Equation on GPU by Jie Liu, Chunye Gong, Weimin Bao, Guojian Tang, Yuewen Jiang

“…We present a parallel GPU solution of the Caputo fractional reaction-diffusion equation in one spatial dimension with explicit finite difference approximation. …”
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A Weak Comparison Principle for Reaction-Diffusion Systems by José Valero

“…We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. …”
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Properness and Topological Degree for Nonlocal Reaction-Diffusion Operators by N. Apreutesei, V. Volpert

“…The paper is devoted to integro-differential operators, which correspond to nonlocal reaction-diffusion equations considered on the whole axis. …”
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Existence of Solutions for a Quasilinear Reaction Diffusion System by Canrong Tian

“…The degenerate reaction diffusion system has been applied to a variety of physical and engineering problems. …”
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Attractor for a Reaction-Diffusion System Modeling Cancer Network by Xueyong Chen, Jianwei Shen, Hongxian Zhou

“…A reaction-diffusion cancer network regulated by microRNA is considered in this paper. …”
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On Asymptotic Behavior for Reaction Diffusion Equation with Small Time Delay by Xunwu Yin

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Pulse Dynamics in a Bistable Reaction-Diffusion System with Chemotaxis by Satoshi Kawaguchi

“…We consider pulse dynamics in a bistable reaction-diffusion system with chemotaxis. We derive the ordinary differential equation of interfaces by applying the multiple scales method to the reaction-diffusion system for examining the effect of the chemotaxis on pulse dynamics in one dimension. …”
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Novel Evaluation of Fuzzy Fractional Cauchy Reaction-Diffusion Equation by Nehad Ali Shah, Essam R. El-Zahar, Hina M. Dutt, Mohammad Asif Arefin

“…Fractional Cauchy reaction-diffusion equations play a significant role in diffusion, and instabilities can lead to formation and stabilization. …”
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An Algebraic Method on the Eigenvalues and Stability of Delayed Reaction-Diffusion Systems by Jian Ma, Baodong Zheng

“…The eigenvalues and stability of the delayed reaction-diffusion systems are considered using the algebraic methods. …”
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Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients by Nauman Raza, Asma Rashid Butt

“…Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. …”
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Morphological spatial patterns in a reaction diffusion model for metal growth by Benedetto Bozzini, Deborah Lacitignola, Ivonne Sgura

“…In this paper a reaction-diffusion system modelling metal growth processes is considered, to investigate -within the electrodeposition context- the formation of morphological patterns in a finite two-dimensional spatialdomain. …”
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