AIMS Mathematics

2020, Issue 1: 96-110. doi: 10.3934/math.2020007
Research article Special Issues

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

• 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.

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

Related Papers:

• 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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沈阳化工大学材料科学与工程学院 沈阳 110142

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