Abstract
We introduce the concepts of \({\cal P}\)-perturbed system and, in particular, \({\cal P}\)-perturbed complex system. Based on the method of Lyapunov functions, we obtain the sufficient condition of total Poisson boundedness of solutions to the \({\cal P}\)-perturbed system with respect to any linear system with constant coefficients. Based on the method of vector Lyapunov functions and the above-stated condition, we obtain sufficient conditions of total Poisson boundedness of solutions to the \({\cal P}\)-perturbed complex system and solutions to the \({\cal P}\)-perturbed complex system with feedback loop.
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Funding
The work was supported by grant no. MK-139.2017.1 of the President of Russian Federation.
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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 10, pp. 62–74.
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Lapin, K.S. Total Poisson Boundedness of Solutions of \({\cal P}\)-Perturbed Complex Systems of Differential Equations. Russ Math. 63, 55–65 (2019). https://doi.org/10.3103/S1066369X19100074
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DOI: https://doi.org/10.3103/S1066369X19100074