https://doi.org/10.1140/epjs/s11734-024-01418-6
Regular Article
Complex spatiotemporal phenomena in multi-dimensional reaction–diffusion system
1
Department of Mathematical Sciences, Federal University of Technology Akure, PMB 704, Akure, Ondo State, Nigeria
2
Department of Decision Sciences, College of Economic and Management Sciences, University of South Africa (UNISA), 003, Pretoria, South Africa
3
Faculty of Data Science and Analytics, Sir Padampat Singhania University, 313601, Udaipur, Rajasthan, India
Received:
8
May
2024
Accepted:
14
November
2024
Published online:
28
November
2024
This study investigates numerical pattern formation process in multi-dimensional Gray–Scott reaction and diffusion systems. While many previous studies have been confined to one-dimensional solutions due to the complexities of high-dimensional numerical solutions, this research emphasizes higher dimensions, where pattern formation becomes significantly interesting. Using finite difference and compact difference methods, the study explores pattern dynamics in two- and three-dimensional spaces. It also provides a mathematical foundation and computational analysis of the model from a biological perspective, offering guidelines on parameter selection through linear stability analysis of both non-diffusive and diffusive systems. Numerical experiments showcased remarkable Turing and spatiotemporal patterns.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
