A competition system with nonlinear cross-diffusion: exact periodic patterns Article Swipe
Róbert Kersner
,
Mihály Klincsik
,
Dinara Zhanuzakova
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1007/s13398-022-01299-1
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1007/s13398-022-01299-1
Our concern in this paper is to shed some additional light on the mechanism and the effect caused by the so called cross-diffusion. We consider a two-species reaction–diffusion (RD) system. Both “fluxes” contain the gradients of both unknown solutions. We show that–for some parameter range– there exist two different type of periodic stationary solutions. Using them, we are able to divide into parts the (eight-dimensional) parameter space and indicate the so called Turing domains where our solutions exist. The boundaries of these domains, in analogy with “bifurcation point”, called “bifurcation surfaces”. As it is commonly believed, these solutions are limits as t goes to infinity of the solutions of corresponding evolution system. In a forthcoming paper we shall give a detailed account about our numerical results concerning different kind of stability. Here we also show some numerical calculations making plausible that our solutions are in fact attractors with a large domain of attraction in the space of initial functions.
Related Topics
Concepts
Attractor
Bifurcation
Parameter space
Domain (mathematical analysis)
Space (punctuation)
Infinity
Diffusion
Statistical physics
Nonlinear system
Stability (learning theory)
Bifurcation theory
Mathematics
Reaction–diffusion system
Mathematical analysis
Physics
Computer science
Geometry
Quantum mechanics
Operating system
Machine learning
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1007/s13398-022-01299-1
- https://link.springer.com/content/pdf/10.1007/s13398-022-01299-1.pdf
- OA Status
- hybrid
- Cited By
- 5
- References
- 9
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4298000836
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4298000836Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1007/s13398-022-01299-1Digital Object Identifier
- Title
-
A competition system with nonlinear cross-diffusion: exact periodic patternsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2022Year of publication
- Publication date
-
2022-09-29Full publication date if available
- Authors
-
Róbert Kersner, Mihály Klincsik, Dinara ZhanuzakovaList of authors in order
- Landing page
-
https://doi.org/10.1007/s13398-022-01299-1Publisher landing page
- PDF URL
-
https://link.springer.com/content/pdf/10.1007/s13398-022-01299-1.pdfDirect link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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hybridOpen access status per OpenAlex
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https://link.springer.com/content/pdf/10.1007/s13398-022-01299-1.pdfDirect OA link when available
- Concepts
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Attractor, Bifurcation, Parameter space, Domain (mathematical analysis), Space (punctuation), Infinity, Diffusion, Statistical physics, Nonlinear system, Stability (learning theory), Bifurcation theory, Mathematics, Reaction–diffusion system, Mathematical analysis, Physics, Computer science, Geometry, Quantum mechanics, Operating system, Machine learningTop concepts (fields/topics) attached by OpenAlex
- Cited by
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5Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1, 2023: 4Per-year citation counts (last 5 years)
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9Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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