This article is cited in 2 papers

First integrals and periodic solutions of a system with power nonlinearities

A. A. Kosov, E. I. Semenov

Matrosov Institute for System Dynamics and Control Theory SB RAS, 134 Lermontov str., 664033 Irkutsk

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 sophisticated models. 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.

Keywords: system of ordinary differential equations, first integral, periodic solution, elliptic Jacobi function.

UDC: 517.946

Received: 17.04.2017

DOI: 10.17377/sibjim.2018.21.105

 English version: Journal of Applied and Industrial Mathematics, 2018, 12:1, 70–83

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