Transition from circular to spiral waves and from Mexican hat to upside-down Mexican hat-solutions: The cases of local and nonlocal λ - ω reaction-diffusion-convection fractal systems with variable coefficients

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60077344%3A_____%2F24%3A00616555" target="_blank" >RIV/60077344:_____/24:00616555 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1016/j.chaos.2024.115737" target="_blank" >https://doi.org/10.1016/j.chaos.2024.115737</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.chaos.2024.115737" target="_blank" >10.1016/j.chaos.2024.115737</a>

Result language

angličtina

Original language name

Transition from circular to spiral waves and from Mexican hat to upside-down Mexican hat-solutions: The cases of local and nonlocal λ - ω reaction-diffusion-convection fractal systems with variable coefficients

Original language description

Nonlinear partial differential equations admitting traveling wave solutions play an important role in the description and analysis of real-life physical processes and nonlinear phenomena. In this study, we prove that the excitable lambda omega reaction-diffusion-convection system introduced by Kopell and Howard can exhibit, in fractal dimensions, a large variety of spatial patterns. We have considered two independent models: a local reactiondiffusion-convection model characterized by variable coefficients that are subject to particular power laws and a nonlocal reaction-diffusion model characterized by symmetric kernels and a variable diffusion coefficient. Each model is characterized by a number of motivating properties and features. In the 1st model, the amplitude is governed by a 2nd-order differential equation, whereas in the 2nd-model, the amplitude is governed by a 4thorder differential equation, which is, under some conditions, comparable to the Swift-Hohenberg equation with variable coefficients that arise in the study of pattern formation, which belongs to the family of extended Fisher-Kolmogorov stationary equations used to study pattern-forming systems in biological and chemical systems. We report the emergence of superstructures that are suppressed for fractal dimensions much less than unity. These superstructures include superspiral waves characterized by a circular symmetry detected in various oscillatory media and the emergence of reflection of waves that take place in non-uniform reaction-diffusion systems, besides the emergence of micro-spiral waves that emerge at the cellular level. A transition from spiral waves to perfectly rotating waves is observed, besides a transition from Mexican hat shaped solutions to upsidedown Mexican hat shaped solutions. The domain size has a very strong impact on the rotational frequency of spiral and circular waves. These new phenomena associated with configuration patterns through a reactiondiffusion-convection system with different scales and characterized by variable coefficients can be applied for modeling a wide class of reaction-diffusion-convection problems. Supplementary properties have been obtained and discussed accordingly.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

<a href="/en/project/QK22020134" target="_blank" >QK22020134: Inovative fisheries management of a large reservoir</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Chaos Solitons & Fractals

ISSN

0960-0779

e-ISSN

1873-2887

Volume of the periodical

189

Issue of the periodical within the volume

Dec

Country of publishing house

GB - UNITED KINGDOM

Number of pages

28

Pages from-to

115737

UT code for WoS article

001359589500001

EID of the result in the Scopus database

2-s2.0-85209135614