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Year 2019, Volume: 68 Issue: 2, 1922 - 1929, 01.08.2019
https://doi.org/10.31801/cfsuasmas.496745

Abstract

References

  • Nicholson, A.J. An outline of the dynamics of animal populations, Australian Journal of Zoology. 2 (1) (1954), 9-65.
  • Gurney, W.S.C., Blythe, S.P. and Nisbet, R.M. Nicholson's blowflies revisited, Nature., 287 (1980), 17-21.
  • Li, J., Global attractivity in Nicholson's blowflies, Appl.Math. J. Chineese Univ. Ser. B. 11 (4) (1996), 425-434.
  • Gyori, I., Trofimchuk, S. Global attractivity in dx/xt=-δx+pf(x(t-τ)), Dynam. Syst. Appl. 8 (1999), 197-210.
  • Gyori, I., Trofimchuk, S. On the existence of rapidly oscillatory solutions in the Nicholson blowflies equation, Nonlinear Anal. 48 (7) (2002), 1033-1042.
  • Chen, Y., Periodic solutions of delayed periodic Nicholson's blowflies models, Can. Appl. Math. Q. 11 (1) (2003), 23-28.
  • Wei, J. and Li, M., Hopf bifurcation analysis in a delayed Nicholson blowflies equation, Nonlinear Anal. 60 (7) (2005), 1351-1367.
  • Li, X. and Fan, Y.H., Existence and global attractivity of positive periodic solutions for the impulsive delay Nicholson's blowflies model, J.Comput.Appl.Math. 201 (2007), 55-68.
  • Berezansky, L., Idels, L. and Troib, L., Global dynamics of Nicholson-type delay systems with applications, Nonlinear Anal. Real World appl. 12 (2011), 436-445.
  • Hien, L.V., Global asymptotic behaviour of positive solutions to a non-autonomous Nicholson's blowflies model with delays, Journal of Biological Dynamics, 8 (1) (2014), 135-144.
  • Berezansky, L., Braverman E. and Idels, L., Nicholson's blowflies differential equations revisited: Main results and open problems, Applied Mathematical Modelling, 34 (2010) 1405-1417.
  • Zhou, H., Wang, W. and Zhang, H., Convergence for a class of non-autonomous Nicholson's blowflies model with time-varying coefficients and delays, Nonlinear Analysis-Real World Applications, 11 (2010), 3431-3436.
  • Gyori, I., Karakoç, F. and Bereketoglu, H., Convergence of solutions of a linear impulsive differential equations system with many delays, Dynamics of Continuous, Discrete and Impulsive Systems Series A., 18 (2011), 191-202.
  • Bereketoğlu, H. and Karakoç, F. Asymptotic constancy for impulsive delay differential equations. Dynamic Systems and Applications, 17 (2008), 71-84.
  • Alzabut, J., Almost periodic solutions for an impulsive delay Nicholson's blowflies model, Journal of Computational and Applied Mathematics, 234 (1) (2010), 233-239.
  • Zhou, H., Wang, J. and Zhou, Z., Positive almost periodic solutions for impulsive Nicholson's blowflies model with multiple linear harvesting terms, Mathematical Models in the Applied Sciences, 36 (4) (2013), 456-461.
  • Dai, B. and Bao, L., Positive periodic solutions generated by impulses for the delay Nicholson's blowflies model, EJQTDE, 4, (2016), 1-11. Samoilenko : Samoilenko, A. M. and Perestyuk, N.A., Impulsive Differential Equations. World Scientific; 1995.
  • Bereketoglu, H. and Oztepe, G.S., Convergence of the solution of an impulsive differential equation with piecewise constant arguments, Miskolc Math. Notes, Vol. 14 No. 3 (2013), 801--815.
  • Bereketoglu, H. and Oztepe, G.S., Asymptotic constancy for impulsive differential equation with piecewise constant arguments, Bull. Math. Soc. Sci. Math. Roumanie, Tome, 57 105 No. 2, (2014), 181-192.

Convergence of solutions of nonautonomous Nicholson's Blowflies model with impulses

Year 2019, Volume: 68 Issue: 2, 1922 - 1929, 01.08.2019
https://doi.org/10.31801/cfsuasmas.496745

Abstract

This paper deals with a nonautonomous Nicholson's blowflies model with impulses. It is shown that under the proper conditions every positive solution of the model approaches to a constant as t tends to infinity.

References

  • Nicholson, A.J. An outline of the dynamics of animal populations, Australian Journal of Zoology. 2 (1) (1954), 9-65.
  • Gurney, W.S.C., Blythe, S.P. and Nisbet, R.M. Nicholson's blowflies revisited, Nature., 287 (1980), 17-21.
  • Li, J., Global attractivity in Nicholson's blowflies, Appl.Math. J. Chineese Univ. Ser. B. 11 (4) (1996), 425-434.
  • Gyori, I., Trofimchuk, S. Global attractivity in dx/xt=-δx+pf(x(t-τ)), Dynam. Syst. Appl. 8 (1999), 197-210.
  • Gyori, I., Trofimchuk, S. On the existence of rapidly oscillatory solutions in the Nicholson blowflies equation, Nonlinear Anal. 48 (7) (2002), 1033-1042.
  • Chen, Y., Periodic solutions of delayed periodic Nicholson's blowflies models, Can. Appl. Math. Q. 11 (1) (2003), 23-28.
  • Wei, J. and Li, M., Hopf bifurcation analysis in a delayed Nicholson blowflies equation, Nonlinear Anal. 60 (7) (2005), 1351-1367.
  • Li, X. and Fan, Y.H., Existence and global attractivity of positive periodic solutions for the impulsive delay Nicholson's blowflies model, J.Comput.Appl.Math. 201 (2007), 55-68.
  • Berezansky, L., Idels, L. and Troib, L., Global dynamics of Nicholson-type delay systems with applications, Nonlinear Anal. Real World appl. 12 (2011), 436-445.
  • Hien, L.V., Global asymptotic behaviour of positive solutions to a non-autonomous Nicholson's blowflies model with delays, Journal of Biological Dynamics, 8 (1) (2014), 135-144.
  • Berezansky, L., Braverman E. and Idels, L., Nicholson's blowflies differential equations revisited: Main results and open problems, Applied Mathematical Modelling, 34 (2010) 1405-1417.
  • Zhou, H., Wang, W. and Zhang, H., Convergence for a class of non-autonomous Nicholson's blowflies model with time-varying coefficients and delays, Nonlinear Analysis-Real World Applications, 11 (2010), 3431-3436.
  • Gyori, I., Karakoç, F. and Bereketoglu, H., Convergence of solutions of a linear impulsive differential equations system with many delays, Dynamics of Continuous, Discrete and Impulsive Systems Series A., 18 (2011), 191-202.
  • Bereketoğlu, H. and Karakoç, F. Asymptotic constancy for impulsive delay differential equations. Dynamic Systems and Applications, 17 (2008), 71-84.
  • Alzabut, J., Almost periodic solutions for an impulsive delay Nicholson's blowflies model, Journal of Computational and Applied Mathematics, 234 (1) (2010), 233-239.
  • Zhou, H., Wang, J. and Zhou, Z., Positive almost periodic solutions for impulsive Nicholson's blowflies model with multiple linear harvesting terms, Mathematical Models in the Applied Sciences, 36 (4) (2013), 456-461.
  • Dai, B. and Bao, L., Positive periodic solutions generated by impulses for the delay Nicholson's blowflies model, EJQTDE, 4, (2016), 1-11. Samoilenko : Samoilenko, A. M. and Perestyuk, N.A., Impulsive Differential Equations. World Scientific; 1995.
  • Bereketoglu, H. and Oztepe, G.S., Convergence of the solution of an impulsive differential equation with piecewise constant arguments, Miskolc Math. Notes, Vol. 14 No. 3 (2013), 801--815.
  • Bereketoglu, H. and Oztepe, G.S., Asymptotic constancy for impulsive differential equation with piecewise constant arguments, Bull. Math. Soc. Sci. Math. Roumanie, Tome, 57 105 No. 2, (2014), 181-192.
There are 19 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Review Articles
Authors

Elif Demirci 0000-0002-7304-8406

Fatma Karakoç 0000-0002-4351-0073

Publication Date August 1, 2019
Submission Date December 18, 2018
Acceptance Date March 19, 2019
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Demirci, E., & Karakoç, F. (2019). Convergence of solutions of nonautonomous Nicholson’s Blowflies model with impulses. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1922-1929. https://doi.org/10.31801/cfsuasmas.496745
AMA Demirci E, Karakoç F. Convergence of solutions of nonautonomous Nicholson’s Blowflies model with impulses. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1922-1929. doi:10.31801/cfsuasmas.496745
Chicago Demirci, Elif, and Fatma Karakoç. “Convergence of Solutions of Nonautonomous Nicholson’s Blowflies Model With Impulses”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1922-29. https://doi.org/10.31801/cfsuasmas.496745.
EndNote Demirci E, Karakoç F (August 1, 2019) Convergence of solutions of nonautonomous Nicholson’s Blowflies model with impulses. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1922–1929.
IEEE E. Demirci and F. Karakoç, “Convergence of solutions of nonautonomous Nicholson’s Blowflies model with impulses”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1922–1929, 2019, doi: 10.31801/cfsuasmas.496745.
ISNAD Demirci, Elif - Karakoç, Fatma. “Convergence of Solutions of Nonautonomous Nicholson’s Blowflies Model With Impulses”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1922-1929. https://doi.org/10.31801/cfsuasmas.496745.
JAMA Demirci E, Karakoç F. Convergence of solutions of nonautonomous Nicholson’s Blowflies model with impulses. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1922–1929.
MLA Demirci, Elif and Fatma Karakoç. “Convergence of Solutions of Nonautonomous Nicholson’s Blowflies Model With Impulses”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1922-9, doi:10.31801/cfsuasmas.496745.
Vancouver Demirci E, Karakoç F. Convergence of solutions of nonautonomous Nicholson’s Blowflies model with impulses. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1922-9.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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