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Rank Two Integral Aspects of Three Dimensional Lotka–Volterra Equations with Nonstandard Analysis

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Abstract

In this paper the problems of integrable and linearizable Lotka–Volterra equations with \((\delta :-3 \delta :\delta )\)–resonance are studied. The necessary conditions for integrability and linearizability have been obtained for the case where \(\delta =1\). A variety of techniques have been used to prove the sufficiency of these necessary conditions. In particular, the linearizable saddle in two variables and majorization in the third variable is used for some cases. Also a nonstandard analysis approach has been used for some integrability aspects of perturbations of the given system.

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Acknowledgements

We sincerely thank Dr. Colin Cristopher (School of Engineering, Computing and Mathematics, Faculty of Science and Engineering, Plymouth University) for very fruitful discussions in solving the Cases 17 and 31. We also thank the referees for very careful reading and also very helpful suggestions.

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  1. Department of Mathematics, College of Science, Salahaddin University-Erbil, Erbil, Kurdistan Region, Iraq

    Chiman Qadir, Waleed Aziz & Ibrahim Hamad

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  1. Chiman Qadir
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  2. Waleed Aziz
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  3. Ibrahim Hamad
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Correspondence to Chiman Qadir.

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Qadir, C., Aziz, W. & Hamad, I. Rank Two Integral Aspects of Three Dimensional Lotka–Volterra Equations with Nonstandard Analysis. Differ Equ Dyn Syst (2023). https://doi.org/10.1007/s12591-023-00664-9

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