Open AccessOn the continuity of the function describing the
times of meeting impulsive set and its application
Author(s) -
Sanyi Tang,
Wenhong Pang
Publication year - 2017
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2017072
Subject(s) - function (biology) , limit (mathematics) , set (abstract data type) , dynamical systems theory , population , planar , mathematics , computer science , control theory (sociology) , control (management) , calculus (dental) , mathematical analysis , physics , artificial intelligence , demography , computer graphics (images) , quantum mechanics , evolutionary biology , sociology , biology , programming language , medicine , dentistry
The properties of the limit sets of orbits of planar impulsive semi-dynamic system strictly depend on the continuity of the function, which describes the times of meeting impulsive sets. In this note, we will show a more realistic counter example on the continuity of this function which has been proven and widely used in impulsive dynamical system and applied in life sciences including population dynamics and disease control. Further, what extra condition should be added to guarantee the continuity of the function has been addressed generally, and then the applications and shortcomings have been discussed when using the properties of this function.