Averaging Principles for Nonautonomous Two-Time-Scale Stochastic Reaction-Diffusion Equations with Jump by Yong Xu, Ruifang Wang

“…In this paper, we aim to develop the averaging principle for a slow-fast system of stochastic reaction-diffusion equations driven by Poisson random measures. …”
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Qualitative Analysis for a Reaction-Diffusion Predator-Prey Model with Disease in the Prey Species by Meihong Qiao, Anping Liu, Urszula Foryś

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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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L1(R)-Nonlinear Stability of Nonlocalized Modulated Periodic Reaction-Diffusion Waves by Soyeun Jung

“…Assuming spectral stability conditions of periodic reaction-diffusion waves u¯(x), we consider L1(R)-nonlinear stability of modulated periodic reaction-diffusion waves, that is, modulational stability, under localized small initial perturbations with nonlocalized initial modulations. …”
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A two or three compartments hyperbolic reaction-diffusion model for the aquatic food chain by Elvira Barbera, Giancarlo Consolo, Giovanna Valenti

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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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Blow-Up Rate Estimates for a System of Reaction-Diffusion Equations with Gradient Terms by Maan A. Rasheed, Hassan Abd Salman Al-Dujaly, Talat Jassim Aldhlki

“…This paper is concerned with the blow-up properties of Cauchy and Dirichlet problems of a coupled system of Reaction-Diffusion equations with gradient terms. The main goal is to study the influence of the gradient terms on the blow-up profile. …”
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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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Asymptotic Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying Delays by Yutian Zhang

“…The provided stability criteria are applicable to Dirichlet boundary condition and showed to be dependent on all of the reaction-diffusion coefficients, the dimension of the space, the delay, and the boundary of the spatial variables. …”
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Adaptive Optimal 𝑚-Stage Runge-Kutta Methods for Solving Reaction-Diffusion-Chemotaxis Systems by Jui-Ling Yu

“…We present a class of numerical methods for the reaction-diffusion-chemotaxis system which is significant for biological and chemistry pattern formation problems. …”
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Stability Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Time-Varying Delays by Chuangxia Huang, Xinsong Yang, Yigang He

“…This paper is concerned with pth moment exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with time-varying delays. …”
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Novel Investigation of Fractional-Order Cauchy-Reaction Diffusion Equation Involving Caputo-Fabrizio Operator by Meshari Alesemi, Naveed Iqbal, Mohammed S. Abdo

“…In this article, the new iterative transform technique and homotopy perturbation transform method are applied to calculate the fractional-order Cauchy-reaction diffusion equation solution. Yang transformation is mixed with the new iteration method and homotopy perturbation method in these methods. …”
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Hopf bifurcation induced by fear: A Leslie-Gower reaction-diffusion predator-prey model by Jiani Jin, Haokun Qi, Bing Liu

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Spatiotemporal Dynamics of a Reaction Diffusive Predator-Prey Model: A Weak Nonlinear Analysis by N. B. Sharmila, C. Gunasundari, Mohammad Sajid

“…This study introduces and investigates a predator-prey model incorporating reaction-diffusion through a system of differential equations. …”
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Exponential Stability and Periodicity of Fuzzy Delayed Reaction-Diffusion Cellular Neural Networks with Impulsive Effect by Guowei Yang, Yonggui Kao, Changhong Wang

“…This paper considers dynamical behaviors of a class of fuzzy impulsive reaction-diffusion delayed cellular neural networks (FIRDDCNNs) with time-varying periodic self-inhibitions, interconnection weights, and inputs. …”
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Stability of Impulsive Cohen-Grossberg Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms by Jinhua Huang, Jiqing Liu, Guopeng Zhou

“…This work concerns the stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms as well as Dirichlet boundary condition. …”
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Stability of Exact and Discrete Energy for Non-Fickian Reaction-Diffusion Equations with a Variable Delay by Dongfang Li, Chao Tong, Jinming Wen

“…This paper is concerned with the stability of non-Fickian reaction-diffusion equations with a variable delay. It is shown that the perturbation of the energy function of the continuous problems decays exponentially, which provides a more accurate and convenient way to express the rate of decay of energy. …”
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A Strongly A-Stable Time Integration Method for Solving the Nonlinear Reaction-Diffusion Equation by Wenyuan Liao

“…The semidiscrete ordinary differential equation (ODE) system resulting from compact higher-order finite difference spatial discretization of a nonlinear parabolic partial differential equation, for instance, the reaction-diffusion equation, is highly stiff. Therefore numerical time integration methods with stiff stability such as implicit Runge-Kutta methods and implicit multistep methods are required to solve the large-scale stiff ODE system. …”
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Hopf Bifurcations and Oscillatory Patterns of a Homogeneous Reaction-Diffusion Singular Predator-Prey Model by Zhenhua Bao, He Liu

“…A kind of homogeneous reaction-diffusion singular predator-prey model with no-flux boundary condition is considered. …”
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Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay by Hua Liu, Yong Ye, Yumei Wei, Weiyuan Ma, Ming Ma, Kai Zhang

“…In this paper, we establish a reaction-diffusion predator-prey model with weak Allee effect and delay and analyze the conditions of Turing instability. …”
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