TY - JOUR

T1 - Orbital stability of periodic solutions of an impulsive system with a linear continuous-time part

AU - Churilov, Alexander N.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - 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.

AB - 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.

KW - Exponential stability

KW - Hybrid systems

KW - Orbital stability

KW - Periodic solutions

KW - Systems with impulses

UR - http://www.scopus.com/inward/record.url?scp=85074235889&partnerID=8YFLogxK

U2 - 10.3934/math.2020007

DO - 10.3934/math.2020007

M3 - Article

AN - SCOPUS:85074235889

VL - 5

SP - 96

EP - 110

JO - AIMS Mathematics

JF - AIMS Mathematics

SN - 2473-6988

IS - 1

ER -