First Integrals and Periodic Solutions of a System with Power Nonlinearities
- Authors: Kosov A.A.1, Semenov E.I.1
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Affiliations:
- Matrosov Institute for System Dynamics and Control Theory
- Issue: Vol 12, No 1 (2018)
- Pages: 70-83
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/212983
- DOI: https://doi.org/10.1134/S1990478918010076
- ID: 212983
Cite item
Abstract
Under consideration is some system of ordinary differential equations with power nonlinearities. These systems are widely used in mathematical biology and chemical kinetics, and can also occur by reduction of more sophisticatedmodels. We formulate conditions on the system parameters which guarantee the existence of first integrals defined by the combinations of power and logarithmic functions of the phase variables. Using the first integrals, we construct periodic solutions for the three-variable systems. A few examples are given illustrating the results.
About the authors
A. A. Kosov
Matrosov Institute for System Dynamics and Control Theory
Author for correspondence.
Email: aakosov@yandex.ru
Russian Federation, ul. Lermontova 134, Irkutsk, 664033
E. I. Semenov
Matrosov Institute for System Dynamics and Control Theory
Email: aakosov@yandex.ru
Russian Federation, ul. Lermontova 134, Irkutsk, 664033