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.
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
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.
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.
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.
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.