Orbital stability of periodic solutions of an impulsive system with a linear continuous-time part
An impulsive system with a linear continuous-time part and a nonlinear discrete-time part is considered. A criterion for exponential orbital stability of its periodic solutions is obtained. The proof is based on linearization by the first approximation of an auxiliary discrete-time system. The formu...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020007/fulltext.html |
| Summary: | An impulsive system with a linear continuous-time part and a nonlinear discrete-time part is considered. A criterion for exponential orbital stability of its periodic solutions is obtained. The proof is based on linearization by the first approximation of an auxiliary discrete-time system. The formulation of the criterion depends significantly on a number of impulses per period of the solution. The paper provides a mathematical rationale for some results previously examined in mathematical biology by computer simulations. |
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| ISSN: | 2473-6988 |