International Journal on Science and Technology

E-ISSN: 2229-7677   •   Impact Factor: 9.88

A Widely Indexed Open Access Peer Reviewed Multidisciplinary Bi-monthly Scholarly International Journal

Call for Paper Volume 17 Issue 4 October-December 2026 Submit your research before last 3 days of December to publish your research paper in the issue of October-December.
Submit Research Paper Join as a Reviewer

Plagiarism is checked by the leading plagiarism checker TurnItIn

Call for Paper

Volume 17 Issue 4
October-December 2026

Submit your research paper

Indexing Partners
Academia Advanced Sciences Index Bielefeld Academic Search Engine CiteSeer DRJI Google Scholar Independent Search Engine & Directory Network ISI (International Scientific Indexing) Issuu Mendeley Research Networks
RefSeek ResearcherId - Thomson Reuters ResearchGate Scirus Scribd Semantic Scholar UTeM - Universiti Teknikal Malaysia Melaka Wiki for Call for Papers WorldCat Zenodo

Reaction-Diffusion Equations: Mathematical Theory, Stability and Pattern Formation

Author(s) Rajesh Kumar
Country India
Abstract At the academic level, a basic approach to mathematic modeling of reactions and diffusion processes is given by the reaction-diffusion equations. This work presents an analysis of reaction-diffusion equations, potentially leading to some interesting results in studying the phenomenon of diffusion instability,which is manifested in formation of spatial patterns. The new system of equations is provided for analysis; the stability analysis of equilibria of selected systems is performed employing linearization and spectral analysis. In this paper, the analysis of the influence of diffusion on stability spectra is conducted with aim to identify the conditions, under which equilibrium point being stable from the viewpoint of stability becomes unstable due to diffusion process. The Turing instability mechanism is studied as a key mechanism for appearance of non-homogeneous stationary structures. In the current research project, typical examples of reaction-diffusion models have been used to illustrate the theoretical framework. In this case, the Schnakenberg model has served as one of the examples included in the research focusing on the identification of equilibrium states and the conditions for instability and calculating characteristic spatial disturbances. The results of the research demonstrate the process of the smallest spatial disturbances’ evolution and formation of stable spatial structures. The analysis reveals the relationships connecting chemical reactions, diffusion coefficients, stability of systems, and pattern formation process.
Keywords Reaction-diffusion equations; Stability analysis; Diffusion-driven instability; Turing instability; Pattern formation; Equilibrium solutions; Linearization; Dispersion relation; Spatial patterns; Schnakenberg model.
Published In Volume 8, Issue 1, January-March 2017
Published On 2017-01-27
DOI https://doi.org/10.71097/IJSAT.v8.i1.11597
View / Download PDF File

Share this


CrossRef

Crossref DOI prefix of IJSAT is 10.71097/IJSAT

Downloads
Research Paper Format Copyright Permission Form and Undertaking Form Cover Page Vol 17 Isu 3Cover Page Vol 17 Isu 2Cover Page Vol 17 Isu 1

All research papers published on this website are licensed under Creative Commons Attribution-ShareAlike 4.0 International License, and all rights belong to their respective authors/researchers.

CC-BY-SA Open Access

About IJSAT
Fees & Payment
Current Issue
Publication Archive 		Submit Research Paper
Track Submission Status
Publication Guidelines
Publication Ethics 		Join as a Reviewer
Editors & Reviewers
Get Reviewer Membership Certi. 		Website/Journal Policies
Usage Policy
Content Policies
Privacy Policy
Contact Us Message on WhatsApp +91-9687-182-185 editor@ijsat.org