A multiscale model for glioma spread including cell-tissue interactions and proliferation by Christian Engwer, Markus Knappitsch, Christina Surulescu

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Effects of Predation-Induced Emigration on a Landscape Ecological Model by James T. Cronin, Nalin Fonseka, Jerome Goddard, Ratnasingham Shivaji, Xiaohuan Xue

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The interplay between models and public health policies: Regional control for a class of spatially structured epidemics (think globally, act locally) by Vincenzo Capasso, Sebastian AniȚa

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Hopf Bifurcation and Turing Instability Analysis for the Gierer–Meinhardt Model of the Depletion Type by Lianchao Gu, Peiliang Gong, Hongqing Wang

“…The reaction diffusion system is one of the important models to describe the objective world. …”
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Hopf Bifurcation for a FitzHugh–Nagumo Model with Time Delay in a Network by Suxia Wang

“…A reaction diffusion system is used to study the interaction between species in a population dynamic system. …”
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Global Behavior of Solutions in a Predator-Prey Cross-Diffusion Model with Cannibalism by Meijun Chen, Shengmao Fu, Xiaoli Yang

“…Firstly, the local stability of nonnegative equilibria for the weakly coupled reaction-diffusion model and strongly coupled cross-diffusion model is discussed. …”
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Numerical Solutions of Certain New Models of the Time-Fractional Gray-Scott by Sami Aljhani, Mohd Salmi Md Noorani, Khaled M. Saad, A. K. Alomari

“…A reaction-diffusion system can be represented by the Gray-Scott model. …”
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Exponential Attractor for a First-Order Dissipative Lattice Dynamical System by Xiaoming Fan

“…We construct an exponential attractor for a first-order dissipative lattice dynamical system arising from spatial discretization of reaction-diffusion equations in ℝ𝑘. And we obtain fractal dimension of the exponential attractor.…”
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Accurate solution estimates for vector difference equations by Rigoberto Medina

“…We also discuss applications of our main results to partial reaction-diffusion difference equations and to a Volterra difference equation.…”
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Global Solutions for an -Component System of Activator-Inhibitor Type by S. Abdelmalek, A. Gouadria, A. Youkana

“…This paper deals with a reaction-diffusion system with fractional reactions modeling -substances into interaction following activator-inhibitor's scheme. …”
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Analysis of a Model Arising from Invasion by Precursor and Differentiated Cells by Xiaojie Hou

“…We study the wave solutions for a degenerated reaction diffusion system arising from the invasion of cells. …”
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Stabilization for a Periodic Predator-Prey System by Sebastian Aniţa, Carmen Oana Tarniceriu

“…A reaction-diffusion system modelling a predator-prey system in a periodic environment is considered. …”
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An existence result for a semipositone problem with a sign changing weight by Jaffar Ali, R. Shivaji

“…We establish an existence result on positive solution for a class of reaction-diffusion equation with semipositone structure. …”
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Computer simulation of synthesis of yttrium aluminum garnet by Feliksas Ivanauskas, Aivaras Kareiva, Bogdanas Lapcun

“…The model is based on the reaction-diffusion equations. The model takes into concideration structure of the initial reaction’s components. …”
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Instability Induced by Cross-Diffusion in a Predator-Prey Model with Sex Structure by Shengmao Fu, Lina Zhang

“…We prove that cross-diffusion can destabilize a uniform positive equilibrium which is stable for the ODE system and for the weakly coupled reaction-diffusion system. As a result, we find that stationary patterns arise solely from the effect of cross-diffusion.…”
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Fujita Exponent for a Nonlinear Degenerate Parabolic Equation with Localized Source by Yulan Wang, Xiaojun Song, Chao Ye

“…This paper is devoted to understand the blow-up properties of reaction-diffusion equations which combine a localized reaction term with nonlinear diffusion. …”
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Optimal Control Problem Governed by an Evolution Equation and Using Bilinear Regular Feedback by Badriah Shuwaysh Alanazi, Maawiya Ould Sidi

“…Using optimization techniques, we show how to approximate the flow of a reaction-diffusion bilinear system by a desired target. …”
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Single Phytoplankton Species Growth with Nonlocal Crowding Effect Caused by Chemosensory Aggregation in a Water Column by Yan Wang, Jinxiang Wang, Xiaobin Yao

“…In this paper, we study the existence of positive steady states for a nonlocal reaction-diffusion model which describes the growth of a single phytoplankton species with nonlocal crowding effect caused by chemosensory aggregation in a water column. …”
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Dynamic Properties of a Forest Fire Model by Na Min, Hongyang Zhang, Zhilin Qu

“…The reaction-diffusion equations have been widely used in physics, chemistry, and other areas. …”
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A New Numerical Method to Solve Some PDEs in the Unit Ball and Comparison with the Finite Element and the Exact Solution by Rajae Malek, Chérif Ziti

“…In this paper, we give a new strategy to extend a numerical approximation method for two-dimensional reaction-diffusion problems. We present numerical results for this type of equations with a known analytical solution to qualify errors for the new method. …”
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