Geodesic
First integrals and periodic solutions of a~system with power nonlinearities
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 1, pp. 47-60

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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. 
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     author = {A. A. Kosov and E. I. Semenov},
     title = {First integrals and periodic solutions of a~system with power nonlinearities},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {47--60},
     publisher = {mathdoc},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2018_21_1_a4/}
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A. A. Kosov; E. I. Semenov. First integrals and periodic solutions of a~system with power nonlinearities. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 1, pp. 47-60. http://geodesic.mathdoc.fr/item/SJIM_2018_21_1_a4/