Dynamic analysis of an impulsive differential equation with time-varying delays

Ying Li; Yuanfu Shao

Applications of Mathematics (2014)

  • Volume: 59, Issue: 1, page 85-98
  • ISSN: 0862-7940

Abstract

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An impulsive differential equation with time varying delay is proposed in this paper. By using some analysis techniques with combination of coincidence degree theory, sufficient conditions for the permanence, the existence and global attractivity of positive periodic solution are established. The results of this paper improve and generalize some previously known results.

How to cite

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Li, Ying, and Shao, Yuanfu. "Dynamic analysis of an impulsive differential equation with time-varying delays." Applications of Mathematics 59.1 (2014): 85-98. <http://eudml.org/doc/260796>.

@article{Li2014,
abstract = {An impulsive differential equation with time varying delay is proposed in this paper. By using some analysis techniques with combination of coincidence degree theory, sufficient conditions for the permanence, the existence and global attractivity of positive periodic solution are established. The results of this paper improve and generalize some previously known results.},
author = {Li, Ying, Shao, Yuanfu},
journal = {Applications of Mathematics},
keywords = {periodic solution; permanence; attractivity; impulse; delay; periodic solution; permanence; attractivity; impulse; delay},
language = {eng},
number = {1},
pages = {85-98},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Dynamic analysis of an impulsive differential equation with time-varying delays},
url = {http://eudml.org/doc/260796},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Li, Ying
AU - Shao, Yuanfu
TI - Dynamic analysis of an impulsive differential equation with time-varying delays
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 85
EP - 98
AB - An impulsive differential equation with time varying delay is proposed in this paper. By using some analysis techniques with combination of coincidence degree theory, sufficient conditions for the permanence, the existence and global attractivity of positive periodic solution are established. The results of this paper improve and generalize some previously known results.
LA - eng
KW - periodic solution; permanence; attractivity; impulse; delay; periodic solution; permanence; attractivity; impulse; delay
UR - http://eudml.org/doc/260796
ER -

References

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  9. Nazarenko, V. G., Influence of delay on auto oscillation in cell population, Biofisika 21 (1976), 352-356. (1976) 
  10. Saker, S. H., Alzabut, J. O., Existence of periodic solutions, global attractivity and oscillation of impulsive delay population model, Nonlinear Anal., Real World Appl. 8 (2007), 1029-1039. (2007) Zbl1124.34054MR2331425
  11. Shao, Y., Dai, B., Luo, Z., 10.1016/j.amc.2010.07.042, Appl. Math. Comput. 217 (2010), 2414-2424. (2010) Zbl1200.92044MR2733684DOI10.1016/j.amc.2010.07.042
  12. Shao, Y., Li, Y., Xu, C., 10.1007/s10440-010-9598-y, Acta Appl. Math. 115 (2011), 105-121. (2011) Zbl1247.34121MR2812979DOI10.1007/s10440-010-9598-y
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