| Title: | Integrability of a family of four-dimensional quadratic Lotka–Volterra complex systems |
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| Authors: | ID Mastev, Ivan (Author)
ID Romanovski, Valery (Author) |
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| Files: |  axioms-15-00297-v2.pdf (361,43 KB)
MD5: 9C31539D499FB49E4E041B7FF5BB684E
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FERI - Faculty of Electrical Engineering and Computer Science
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| Abstract: | This work addresses the integrability of four-dimensional quadratic Lotka–Volterra systems exhibiting (1:−1:i:−i) resonance by identifying the parameter constraints required for such properties to exist. Our results show that, within this family, integrability is connected to linearizability and time-reversibility. To establish these results, we combine theoretical and computational methods. On the theoretical side, we use Poincaré–Dulac normal form theory and methods based on Gröbner basis theory. On the computational side, we apply the algorithms described in the paper to compute normal forms and minimal associated prime ideals required for the analysis of the integrability conditions. |
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| Keywords: | integrability, linearizability, normal forms, time-reversibility, polynomial systems of ODEs |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 24.03.2026 |
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| Article acceptance date: | 17.04.2026 |
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| Publication date: | 17.04.2026 |
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| Publisher: | MDPI |
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| Year of publishing: | 2026 |
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| Number of pages: | 17 str. |
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| Numbering: | Vol. 15, issue 4, [article no.] 297 |
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| PID: | 20.500.12556/DKUM-98092  |
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| UDC: | 51 |
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| ISSN on article: | 2075-1680 |
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| COBISS.SI-ID: | 278060803 |
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| DOI: | 10.3390/axioms15040297 |
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| Copyright: | © 2026 by the authors |
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| Publication date in DKUM: | 15.05.2026 |
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| Views: | 151 |
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| Downloads: | 8 |
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| Metadata: |    |
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| Categories: | Misc.
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