☆ 4.5 Article

A domain-dependent stability analysis of reaction-diffusion systems with linear cross-diffusion on circular domains

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2024)

相关参考文献

注意：仅列出部分参考文献，下载原文获取全部文献信息。

Article Mathematics, Interdisciplinary Applications

Cross-diffusion induced Turing patterns on multiplex networks of a predator-prey model

Mingrui Song et al.

Summary: Predator-prey models have attracted attention in various disciplines and the theory of pattern formation in monolayer networks has been extensively studied. This study extends the theory to multiplex networks, which are common in diverse areas. Furthermore, the model is enhanced with cross-diffusion to account for specific movement tendencies of each species. The linear analysis reveals the theoretical Turing instability region and demonstrates that either the multiplex network topology or cross-diffusion can destabilize the homogeneous fixed point, resulting in various Turing patterns. The experimental simulation results confirm the validity of the theoretical analysis.

CHAOS SOLITONS & FRACTALS (2023)

添加到收藏夹

Article Mathematics, Applied

MODELING BACTERIAL TRAVELING WAVE PATTERNS WITH EXACT CROSS-DIFFUSION AND POPULATION GROWTH

Yong-Jung Kim et al.

Summary: Keller-Segel equations are widely used for explaining chemotaxis-induced bacterial traveling band phenomena. This paper presents a chemotaxis model that incorporates cross-diffusion and population growth, particularly focusing on the case where the diffusion and advection terms form an exact cross-diffusion. The mathematical models developed are based on the dynamics of conversion between active and inactive cells with different dispersal rates. The performance of each step in the process is evaluated by comparing numerical simulations and experimental data.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B (2023)

添加到收藏夹

Article Mathematics, Applied

Matrix-oriented FEM formulation for reaction-diffusion PDEs on a large class of 2D domains

Massimo Frittelli et al.

Applied Numerical Mathematics (2023)

添加到收藏夹

Article Mathematics, Applied

Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision

N. Bellomo et al.

Summary: This paper focuses on exotic chemotaxis and cross-diffusion models in complex environments, discussing their derivation, characteristics, and potential new models. It also examines analytical problems in applying these models to real-world dynamics and explores research perspectives in a multiscale vision.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2022)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Cross diffusion induced spatiotemporal pattern in diffusive nutrient-plankton model with nutrient recycling

Sarita Kumari et al.

Summary: This paper presents a mathematical model of spatiotemporal interaction between nutrient and phytoplankton, considering functional response and nutrient recycling, as well as the effects of cross and self-diffusion. Stability analysis and simulation techniques are used to study the systems, and the impact of time evolution, cross-diffusion, and toxin release by phytoplankton on species density distribution is observed. Weakly nonlinear analysis and amplitude equations are introduced to describe the structural interpretation and stability of Turing pattern. Cross-diffusion plays a crucial role in Turing instability and the formation of spot, stripe, and spot-stripe like patterns, suggesting positive environmental outcomes in the real world.

MATHEMATICS AND COMPUTERS IN SIMULATION (2022)

添加到收藏夹

Article Engineering, Mechanical

Cross-diffusion induced spatiotemporal patterns in Schnakenberg reaction-diffusion model

Rui Yang

Summary: This paper investigates the Turing instability conditions driven by cross-diffusion in the Schnakenberg system and reveals that long-range inhibition and short-range activation are no longer necessary for Turing instability with the introduction of cross-diffusion. The amplitude equations at the critical value of Turing bifurcation are derived using the multiple scales method, which helps to determine the parameter space where certain patterns emerge. Numerical simulations in the Turing instability region and Turing-Hopf region demonstrate the variety of patterns that the system can exhibit, and different initial conditions are employed to enhance understanding of the complex patterns.

NONLINEAR DYNAMICS (2022)

添加到收藏夹

Article Physics, Multidisciplinary

Turing and wave instabilities in hyperbolic reaction-diffusion systems: The role of second-order time derivatives and cross-diffusion terms on pattern formation

Joshua S. Ritchie et al.

Summary: This study explores diffusive instabilities and resulting pattern formation in hyperbolic reaction-diffusion equations, finding that additional temporal terms affect the formation and existence regions of Turing patterns, and are necessary for the emergence of spatiotemporal patterns under wave instability. The parameters leading to wave instabilities are mutually exclusive to those leading to stationary Turing patterns.

ANNALS OF PHYSICS (2022)

添加到收藏夹

Article Mathematics

A competition system with nonlinear cross-diffusion: exact periodic patterns

Robert Kersner et al.

Summary: The paper focuses on the mechanism and effect of cross-diffusion in a two-species reaction-diffusion system. It identifies two different types of periodic stationary solutions within a certain parameter range and divides the parameter space to determine the existence of these solutions in Turing domains. The solutions are believed to be the limits of corresponding evolution system solutions as time approaches infinity. Numerical calculations suggest that the solutions are attractors with a large domain of attraction.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS (2022)

添加到收藏夹

Article Mathematics, Interdisciplinary Applications

Turing pattern analysis of a reaction-diffusion rumor propagation system with time delay in both network and non-network environments

Junlang Hu et al.

Summary: The research focuses on the spatio-temporal dynamics of rumor propagation, proposing a reaction-diffusion rumor spreading system and conducting numerical simulations. The effects of diffusion and delay on the shapes of patterns are explored, leading to the discovery of spiral patterns. The validity of the model is verified through fitting with real data.

CHAOS SOLITONS & FRACTALS (2021)

添加到收藏夹

Article Mathematics, Applied

Bulk-surface virtual element method for systems of PDEs in two-space dimensions

Massimo Frittelli et al.

Summary: This paper examines a coupled bulk-surface PDE in two dimensions and presents a novel method, the bulk-surface virtual element method, which demonstrates second-order convergence under certain conditions.

NUMERISCHE MATHEMATIK (2021)

添加到收藏夹

Article Mathematics

Turing instability of the periodic solutions for reaction-diffusion systems with cross-diffusion and the patch model with cross-diffusion-like coupling

Fengqi Yi

Summary: This paper investigates how diffusion can destabilize spatially homogeneous periodic solutions, known as Turing instability. Formulas are established to determine Turing instability of periodic solutions with different diffusion rates, and an example of a chemical reaction model is provided to demonstrate the application of the results.

JOURNAL OF DIFFERENTIAL EQUATIONS (2021)

添加到收藏夹

Article Mathematics, Applied

Cross-diffusion-induced patterns in an SIR epidemic model on complex networks

Lili Chang et al.

CHAOS (2020)

添加到收藏夹

Article Mathematics, Interdisciplinary Applications

Characterizing the Effects of Self- and Cross-Diffusion on Stationary Patterns of a Predator-Prey System

Jia-Fang Zhang et al.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2020)

添加到收藏夹

Article Engineering, Multidisciplinary

Stability Analysis and Parameter Classification of a Reaction-Diffusion Model on an Annulus

Wakil Sarfaraz et al.

JOURNAL OF APPLIED NONLINEAR DYNAMICS (2020)

添加到收藏夹

Article Physics, Multidisciplinary

Turing patterns of an SI epidemic model with cross-diffusion on complex networks

Moran Duan et al.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS (2019)

添加到收藏夹

Article Biology

Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds

Andrew L. Krause et al.

BULLETIN OF MATHEMATICAL BIOLOGY (2019)

添加到收藏夹

Article Engineering, Multidisciplinary

Cross-diffusion effects on a morphochemical model for electrodeposition

Deborah Lacitignola et al.

APPLIED MATHEMATICAL MODELLING (2018)

添加到收藏夹

Article Mathematics, Interdisciplinary Applications

Domain-Dependent Stability Analysis of a Reaction-Diffusion Model on Compact Circular Geometries

Wakil Sarfaraz et al.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2018)

添加到收藏夹

Article Mathematics, Interdisciplinary Applications

Classification of parameter spaces for a reaction-diffusion model on stationary domains

Wakil Sarfaraz et al.

CHAOS SOLITONS & FRACTALS (2017)

添加到收藏夹

Article Mathematics, Applied

Turing pattern formation on the sphere for a morphochemical reaction-diffusion model for electrodeposition

Deborah Lacitignola et al.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2017)

添加到收藏夹

Article Physics, Mathematical

Projected Finite Elements for Systems of Reaction-Diffusion Equations on Closed Evolving Spheroidal Surfaces

Necibe Tuncer et al.

COMMUNICATIONS IN COMPUTATIONAL PHYSICS (2017)

添加到收藏夹

Article Mathematics, Applied

STABILITY ANALYSIS OF REACTION-DIFFUSION MODELS ON EVOLVING DOMAINS: THE EFFECTS OF CROSS-DIFFUSION

Anotida Madzvamuse et al.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (2016)

添加到收藏夹

Article Biology

Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations

Anotida Madzvamuse et al.

JOURNAL OF MATHEMATICAL BIOLOGY (2015)

添加到收藏夹

Article Physics, Fluids & Plasmas

Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces

A. Madzvamuse et al.

PHYSICAL REVIEW E (2014)

添加到收藏夹

Article Mathematics, Applied

IMPLICIT-EXPLICIT TIMESTEPPING WITH FINITE ELEMENT APPROXIMATION OF REACTION-DIFFUSION SYSTEMS ON EVOLVING DOMAINS

Omar Lakkis et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2013)

添加到收藏夹

Article Biology

The surface finite element method for pattern formation on evolving biological surfaces

R. Barreira et al.

JOURNAL OF MATHEMATICAL BIOLOGY (2011)

添加到收藏夹

Article Physics, Fluids & Plasmas

Amplitude equations for reaction-diffusion systems with cross diffusion

Evgeny P. Zemskov et al.

PHYSICAL REVIEW E (2011)

添加到收藏夹

Article Engineering, Multidisciplinary

Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities

Christophe Geuzaine et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2009)

添加到收藏夹

Article Developmental Biology

Pattern formation mechanisms in reaction-diffusion systems

Vladimir K. Vanag et al.

INTERNATIONAL JOURNAL OF DEVELOPMENTAL BIOLOGY (2009)

添加到收藏夹

Review Chemistry, Physical

Cross-diffusion and pattern formation in reaction-diffusion systems

Vladimir K. Vanag et al.

PHYSICAL CHEMISTRY CHEMICAL PHYSICS (2009)

添加到收藏夹

Article Physics, Fluids & Plasmas

Modeling the skin pattern of fishes

Rafael A. Barrio et al.

PHYSICAL REVIEW E (2009)

添加到收藏夹

Review Mathematics, Applied

Partial differential equations for self-organization in cellular and developmental biology

R. E. Baker et al.

NONLINEARITY (2008)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Velocity-induced numerical solutions of reaction-diffusion systems on continuously growing domains

Anotida Madzvamuse et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2007)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains

A Madzvamuse

JOURNAL OF COMPUTATIONAL PHYSICS (2006)

添加到收藏夹

Article Biology

Turing instabilities in general systems

RA Satnoianu et al.

JOURNAL OF MATHEMATICAL BIOLOGY (2000)

添加到收藏夹

© Peeref 2019-2024. All rights reserved.