Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case
Many processes are mathematically simulated by systems of discrete equations with quadratic right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete auto...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/539087 |
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| _version_ | 1832553310704369664 |
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| author | Josef Diblík Denys Ya. Khusainov Irina V. Grytsay Zdenĕk Šmarda |
| author_facet | Josef Diblík Denys Ya. Khusainov Irina V. Grytsay Zdenĕk Šmarda |
| author_sort | Josef Diblík |
| collection | DOAJ |
| description | Many processes are mathematically simulated by systems of discrete equations with quadratic
right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalue λ=1 of the matrix of linear terms. In addition to the stability investigation, we
also estimate stability domains. |
| format | Article |
| id | doaj-art-07f47d7a2e04494fa9cf685b44fb754b |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-07f47d7a2e04494fa9cf685b44fb754b2025-02-03T05:54:15ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/539087539087Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical CaseJosef Diblík0Denys Ya. Khusainov1Irina V. Grytsay2Zdenĕk Šmarda3Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, 616 00 Brno, Czech RepublicDepartment of Complex System Modeling, Faculty of Cybernetics, Taras, Shevchenko National University of Kyiv, Vladimirskaya Str., 64, 01033 Kyiv, UkraineDepartment of Complex System Modeling, Faculty of Cybernetics, Taras, Shevchenko National University of Kyiv, Vladimirskaya Str., 64, 01033 Kyiv, UkraineDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, 616 00 Brno, Czech RepublicMany processes are mathematically simulated by systems of discrete equations with quadratic right-hand sides. Their stability is thought of as a very important characterization of the process. In this paper, the method of Lyapunov functions is used to derive classes of stable quadratic discrete autonomous systems in a critical case in the presence of a simple eigenvalue λ=1 of the matrix of linear terms. In addition to the stability investigation, we also estimate stability domains.http://dx.doi.org/10.1155/2010/539087 |
| spellingShingle | Josef Diblík Denys Ya. Khusainov Irina V. Grytsay Zdenĕk Šmarda Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case Discrete Dynamics in Nature and Society |
| title | Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case |
| title_full | Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case |
| title_fullStr | Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case |
| title_full_unstemmed | Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case |
| title_short | Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case |
| title_sort | stability of nonlinear autonomous quadratic discrete systems in the critical case |
| url | http://dx.doi.org/10.1155/2010/539087 |
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