Orbital stability of periodic solutions of an impulsive system with a linear continuous-time part

Alexander N. Churilov; Alexander N. Churilov

doi:10.3934/math.2020007

AIMS Mathematics

2020, Volume 5, Issue 1: 96-110. doi: 10.3934/math.2020007

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Orbital stability of periodic solutions of an impulsive system with a linear continuous-time part

Alexander N. Churilov ^,

Faculty of Mathematics and Mechanics, St. Petersburg State University, Universitetsky av. 28, Stary Peterhof, 198504, St. Petersburg, Russia

Received: 22 June 2019 Accepted: 14 October 2019 Published: 21 October 2019
MSC : 34A37, 34K13, 34K20

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.
- systems with impulses,
- hybrid systems,
- periodic solutions,
- exponential stability,
- orbital stability
Citation: Alexander N. Churilov. Orbital stability of periodic solutions of an impulsive system with a linear continuous-time part[J]. AIMS Mathematics, 2020, 5(1): 96-110. doi: 10.3934/math.2020007

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Abstract

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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