×

zbMATH — the first resource for mathematics

Positive periodic solutions of Nicholson-type delay systems with nonlinear density-dependent mortality terms. (English) Zbl 1260.34149
Summary: This paper is concerned with the periodic solutions for a class of Nicholson-type delay systems with nonlinear density-dependent mortality terms. By using coincidence degree theory, some criteria are obtained to guarantee the existence of positive periodic solutions of the model. Moreover, an example and a numerical simulation are given to illustrate our main results.

MSC:
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D25 Population dynamics (general)
34K13 Periodic solutions to functional-differential equations
47N20 Applications of operator theory to differential and integral equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] M. de la Sen and N. Luo, “On the uniform exponential stability of a wide class of linear time-delay systems,” Journal of Mathematical Analysis and Applications, vol. 289, no. 2, pp. 456-476, 2004. · Zbl 1046.34086 · doi:10.1016/j.jmaa.2003.08.048
[2] M. de la Sen, “Stability of impulsive time-varying systems and compactness of the operators mapping the input space into the state and output spaces,” Journal of Mathematical Analysis and Applications, vol. 321, no. 2, pp. 621-650, 2006. · Zbl 1111.93072 · doi:10.1016/j.jmaa.2005.08.038
[3] H. Lu and W. Wang, “Dynamics of a nonautonomous Leslie-Gower type food chain model with delays,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 380279, 19 pages, 2011. · Zbl 1213.37126 · doi:10.1155/2011/380279 · eudml:224252
[4] X. Fan, Z. Wang, and F. Jiang, “Dynamics of mutualism-competition-predator system with Beddington-DeAngelis functional responses and impulsive perturbations,” Abstract and Applied Analysis, vol. 2012, Article ID 963486, 33 pages, 2012. · Zbl 1253.92046 · doi:10.1155/2012/963486
[5] L. Berezansky, E. Braverman, and L. Idels, “Nicholson’s blowflies differential equations revisited: main results and open problems,” Applied Mathematical Modelling, vol. 34, no. 6, pp. 1405-1417, 2010. · Zbl 1193.34149 · doi:10.1016/j.apm.2009.08.027
[6] L. Berezansky, L. Idels, and L. Troib, “Global dynamics of Nicholson-type delay systems with applications,” Nonlinear Analysis: Real World Applications, vol. 12, no. 1, pp. 436-445, 2011. · Zbl 1208.34120 · doi:10.1016/j.nonrwa.2010.06.028
[7] W. Wang, L. Wang, and W. Chen, “Existence and exponential stability of positive almost periodic solution for Nicholson-type delay systems,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 1938-1949, 2011. · Zbl 1232.34111 · doi:10.1016/j.nonrwa.2010.12.010
[8] B. Liu, “The existence and uniqueness of positive periodic solutions of Nicholson-type delay systems,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3145-3151, 2011. · Zbl 1231.34119 · doi:10.1016/j.nonrwa.2011.05.014
[9] B. Liu and S. Gong, “Permanence for Nicholson-type delay systems with nonlinear density-dependent mortality terms,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 1931-1937, 2011. · Zbl 1232.34109 · doi:10.1016/j.nonrwa.2010.12.009
[10] W. Wang, “Positive periodic solutions of delayed Nicholson’s blowflies models with a nonlinear density-dependent mortality term,” Applied Mathematical Modelling, vol. 36, no. 10, pp. 4708-4713, 2012. · Zbl 1252.34080 · doi:10.1016/j.apm.2011.12.001
[11] X. Hou and L. Duan, “New results on periodic solutions of delayed Nicholson’s blowflies models,” Electronic Journal of Qualitative Theory of Differential Equations, no. 24, pp. 1-11, 2012. · Zbl 1340.34317
[12] X. Hou, L. Duan, and Z. Huang, “Permanence and periodic solutions for a class of delay Nicholson’s blowflies models,” Applied Mathematical Modelling, vol. 37, pp. 1537-1544, 2013. · Zbl 1351.34088 · doi:10.1016/j.apm.2012.04.018
[13] Z. Chen, “Periodic solutions for Nicholson-type delay system with nonlinear density-dependent mortalityterms,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 56, pp. 1-9, 2012.
[14] R. E. Gaines and J. L. Mawhin, Coincidence Degree, and Nonlinear Differential Equations, vol. 568 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1977. · Zbl 0339.47031 · doi:10.1007/BFb0089538
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.