Unpredictable Solutions of Linear Impulsive Systems

Marat Akhmet, Madina Tleubergenova, Mehmet Onur Fen and Zakhira Nugayeva
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Marat Akhmet: Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey
Madina Tleubergenova: Department of Mathematics, Aktobe Regional University, Aktobe 030000, Kazakhstan
Mehmet Onur Fen: Department of Mathematics, TED University, 06420 Ankara, Turkey
Zakhira Nugayeva: Department of Mathematics, Aktobe Regional University, Aktobe 030000, Kazakhstan

Mathematics, 2020, vol. 8, issue 10, 1-16

Abstract: We consider a new type of oscillations of discontinuous unpredictable solutions for linear impulsive nonhomogeneous systems. The models under investigation are with unpredictable perturbations. The definition of a piecewise continuous unpredictable function is provided. The moments of impulses constitute a newly determined unpredictable discrete set. Theoretical results on the existence, uniqueness, and stability of discontinuous unpredictable solutions for linear impulsive differential equations are provided. We benefit from the B-topology in the space of discontinuous functions on the purpose of proving the presence of unpredictable solutions. For constructive definitions of unpredictable components in examples, randomly determined unpredictable sequences are newly utilized. Namely, the construction of a discontinuous unpredictable function is based on an unpredictable sequence determined by a discrete random process, and the set of discontinuity moments is realized by the logistic map. Examples with numerical simulations are presented to illustrate the theoretical results.

Keywords: discontinuous unpredictable function; linear impulsive system; discontinuous unpredictable solution; asymptotic stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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