AIMS Mathematics, 2020, 5(1): 96-110. doi: 10.3934/math.2020007 Research article Special Issues

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

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

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Special Issues: Initial and Boundary Value Problems for Differential Equations

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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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