Spatially heterogeneous invasion of toxic plant mediated by herbivory by Zhilan Feng, Wenzhang Huang, Donald L. DeAngelis

Subjects: Get full text

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

Subjects: Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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.…”
Get full text

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. …”
Get full text

Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics by Robert Artebrant

“…We study Hopf bifurcation solutions to the Monodomain model equipped with FitzHugh-Nagumo cell dynamics. This reaction-diffusion system plays an important role in the field of electrocardiology as a tractable mathematical model of the electrical activity in the human heart. …”
Get full text

Control of Chaotic Calcium Oscillations in Biological Cells by Quanbao Ji, Min Ye

“…The contribution of this present paper is to propose a method that combines a chemical Brusselator reaction-diffusion system with a biological cell system via gap junction for controlling and visualizing the frequency and magnitude of chaotic intracellular calcium oscillations in two cell types, including nonexcitable cells and the glial cells. …”
Get full text

Stability and Coexistence of a Diffusive Predator-Prey System with Nonmonotonic Functional Response and Fear Effect by Xiaozhou Feng, Hao Sun, Yangfan Xiao, Feng Xiao

“…Finally, the existence and nonexistence of nonconstant positive steady states of this reaction-diffusion system are established by the Leray–Schauder degree theory and Poincaré inequality.…”
Get full text

Analysis of Wave Solutions of an Adhenovirus-Tumor Cell System by Baba Issa Camara, Houda Mokrani

“…We discuss biological background and mathematical analysis of glioma gene therapy for contributing to cancer treatment. By a reaction-diffusion system, we model interactions between gliom cells and viruses. …”
Get full text

The impact of immune cell interactions on virus quasi-species formation by Ali Moussaoui, Vitaly Volpert

“…The process of viral infection spreading in tissues was influenced by various factors, including virus replication within host cells, transportation, and the immune response. Reaction-diffusion systems provided a suitable framework for examining this process. …”
Get full text

Stability in a Simple Food Chain System with Michaelis-Menten Functional Response and Nonlocal Delays by Wenzhen Gan, Canrong Tian, Qunying Zhang, Zhigui Lin

“…This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. …”
Get full text

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. …”
Get full text

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. …”
Get full text

Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions by Sulasri Suddin, Fajar Adi-Kusumo, Lina Aryati, Gunardi

“…We provide an analytical study for the constant equilibria of the reaction-diffusion system describing the above interactions, which show the initial behaviour of the tissue, and we conduct numerical simulation that shows the dynamics along the tissue that represent the immunotherapy effects. …”
Get full text

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. …”
Get full text

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.…”
Get full text

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. …”
Get full text