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

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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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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

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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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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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A reaction-diffusion system modeling the spread of resistance to an antimalarial drug by Nicolas Bacaër, Cheikh Sokhna

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Numerical Simulation and Symmetry Reduction of a Two-Component Reaction-Diffusion System by Jina Li, Xuehui Ji

“…In this paper, the symmetry classification and symmetry reduction of a two-component reaction-diffusion system are investigated, the reaction-diffusion system can be reduced to system of ordinary differential equations, and the solutions and numerical simulation will be showed by examples.…”
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Upper semicontinuity of the attractor for lattice dynamical systems of partly dissipative reaction diffusion systems by Ahmed Y. Abdallah

“…We investigate the existence of a global attractor and its upper semicontinuity for the infinite-dimensional lattice dynamical system of a partly dissipative reaction diffusion system in the Hilbert space l2×l2. Such a system is similar to the discretized FitzHugh-Nagumo system in neurobiology, which is an adequate justification for its study.…”
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Lower Bound for the Blow-Up Time for the Nonlinear Reaction-Diffusion System in High Dimensions by Baiping Ouyang, Wei Fan, Yiwu Lin

“…In this paper, we study the blow-up phenomenon for a nonlinear reaction-diffusion system with time-dependent coefficients under nonlinear boundary conditions. …”
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A Hopf Bifurcation in a Three-Component Reaction-Diffusion System with a Chemoattraction by YoonMee Ham, Sang-Gu Lee, Quoc Phong Vu

“…We consider a three-component reaction-diffusion system with a chemoattraction. The purpose of this work is to analyze the chemotactic effects due to the gradient of the chemotactic sensitivity and the shape of the interface. …”
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A necessary and sufficient condition for global existence for a quasilinear reaction-diffusion system by Alan V. Lair

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Necessary conditions for local and global existence to a reaction-diffusion system with fractional derivatives by Kamel Haouam, Mourad Sfaxi

“…We give some necessary conditions for local and global existence of a solution to reaction-diffusion system of type (FDS) with temporal and spacial fractional derivatives. …”
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Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach by Yonggui Kao, Hamid Reza Karimi

“…This paper is devoted to investigating stability in mean of partial variables for coupled stochastic reaction-diffusion systems on networks (CSRDSNs). By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential equations (SODE) and using Itô formula, we establish some novel stability principles for uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, and exponential stability in mean of partial variables for CSRDSNs. …”
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Analytical Solution of Nonlinear Dynamics of a Self-Igniting Reaction-Diffusion System Using Modified Adomian Decomposition Method by Felicia Shirly Peace, Narmatha Sathiyaseelan, Lakshmanan Rajendran

“…A mathematical model of the dynamics of the self-ignition of a reaction-diffusion system is studied in this paper. An approximate analytical method (modified Adomian decomposition method) is used to solve nonlinear differential equations under steady-state condition. …”
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Calcium waves with mechano-chemical couplings by Bogdan Kazmierczak, Zbigniew Peradzynski

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Flow invariance for perturbed nonlinear evolution equations by Dieter Bothe

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A note on the replicator equation with explicit space and global regulation by Alexander S. Bratus, Vladimir P. Posvyanskii, Artem S. Novozhilov

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Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks by Maya Mincheva, Gheorghe Craciun

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