Unpredictable Solutions of Linear Impulsive Systems
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 const...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-10-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/8/10/1798 |
| _version_ | 1797550833808703488 |
|---|---|
| author | Marat Akhmet Madina Tleubergenova Mehmet Onur Fen Zakhira Nugayeva |
| author_facet | Marat Akhmet Madina Tleubergenova Mehmet Onur Fen Zakhira Nugayeva |
| author_sort | Marat Akhmet |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T15:35:04Z |
| format | Article |
| id | doaj.art-fbd2f37e60b8410ea6ac560f911c043d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:35:04Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-fbd2f37e60b8410ea6ac560f911c043d2023-11-20T17:19:30ZengMDPI AGMathematics2227-73902020-10-01810179810.3390/math8101798Unpredictable Solutions of Linear Impulsive SystemsMarat Akhmet0Madina Tleubergenova1Mehmet Onur Fen2Zakhira Nugayeva3Department of Mathematics, Middle East Technical University, 06800 Ankara, TurkeyDepartment of Mathematics, Aktobe Regional University, Aktobe 030000, KazakhstanDepartment of Mathematics, TED University, 06420 Ankara, TurkeyDepartment of Mathematics, Aktobe Regional University, Aktobe 030000, KazakhstanWe 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.https://www.mdpi.com/2227-7390/8/10/1798discontinuous unpredictable functionlinear impulsive systemdiscontinuous unpredictable solutionasymptotic stability |
| spellingShingle | Marat Akhmet Madina Tleubergenova Mehmet Onur Fen Zakhira Nugayeva Unpredictable Solutions of Linear Impulsive Systems Mathematics discontinuous unpredictable function linear impulsive system discontinuous unpredictable solution asymptotic stability |
| title | Unpredictable Solutions of Linear Impulsive Systems |
| title_full | Unpredictable Solutions of Linear Impulsive Systems |
| title_fullStr | Unpredictable Solutions of Linear Impulsive Systems |
| title_full_unstemmed | Unpredictable Solutions of Linear Impulsive Systems |
| title_short | Unpredictable Solutions of Linear Impulsive Systems |
| title_sort | unpredictable solutions of linear impulsive systems |
| topic | discontinuous unpredictable function linear impulsive system discontinuous unpredictable solution asymptotic stability |
| url | https://www.mdpi.com/2227-7390/8/10/1798 |
| work_keys_str_mv | AT maratakhmet unpredictablesolutionsoflinearimpulsivesystems AT madinatleubergenova unpredictablesolutionsoflinearimpulsivesystems AT mehmetonurfen unpredictablesolutionsoflinearimpulsivesystems AT zakhiranugayeva unpredictablesolutionsoflinearimpulsivesystems |