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

Yıl 2019, Cilt: 68 Sayı: 2, 1922 - 1929, 01.08.2019

Elif Demirci Fatma Karakoç

https://doi.org/10.31801/cfsuasmas.496745

Öz

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.

Anahtar Kelimeler

Nicholson's blowflies model, Convergence, Delay, Impulse

Kaynakça

• 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.