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Existence and stability of positive periodic solutions for a neutral multispecies logarithmic population model with feedback control and impulse. (English) Zbl 1470.34179

Summary: We investigate a neutral multispecies logarithmic population model with feedback control and impulse. By applying the contraction mapping principle and some inequality techniques, a set of easily applicable criteria for the existence, uniqueness, and global attractivity of positive periodic solution are established. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases. We also give an example to illustrate the applicability of our results.

MSC:

34K13 Periodic solutions to functional-differential equations
34K45 Functional-differential equations with impulses
92D25 Population dynamics (general)
93B52 Feedback control
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[1] Weng, P., Existence and global stability of positive periodic solution of periodic integrodifferential systems with feedback controls, Computers & Mathematics with Applications, 40, 6-7, 747-759 (2000) · Zbl 0962.45003
[2] Yang, F.; Jiang, D. Q., Existence and global attractivity of positive periodic solution of a Logistic growth system with feedback control and deviating arguments, Annals of Differential Equations, 17, 4, 337-384 (2001) · Zbl 1004.34030
[3] Chen, F., Positive periodic solutions of neutral Lotka-Volterra system with feedback control, Applied Mathematics and Computation, 162, 3, 1279-1302 (2005) · Zbl 1125.93031
[4] Wang, C.; Shi, J., Periodic solution for a delay multispecies logarithmic population model with feedback control, Applied Mathematics and Computation, 193, 1, 257-265 (2007) · Zbl 1193.34144
[5] Hu, H.; Teng, Z.; Jiang, H., Permanence of the nonautonomous competitive systems with infinite delay and feedback controls, Nonlinear Analysis: Real World Applications, 10, 4, 2420-2433 (2009) · Zbl 1163.45302
[6] Yan, J.; Zhao, A., Oscillation and stability of linear impulsive delay differential equations, Journal of Mathematical Analysis and Applications, 227, 1, 187-194 (1998) · Zbl 0917.34060
[7] Zhang, W.; Fan, M., Periodicity in a generalized ecological competition system governed by impulsive differential equations with delays, Mathematical and Computer Modelling, 39, 4-5, 479-493 (2004) · Zbl 1065.92066
[8] Wang, Q.; Dai, B. X., Existence of positive periodic solutions for a neutral population model with delays and impulse, Nonlinear Analysis: Theory, Methods and Applications, 69, 3919-3930 (2008) · Zbl 1166.34047
[9] Zhang, Y.; Sun, J., Stability of impulsive functional differential equations, Nonlinear Analysis: Theory, Methods & Applications, 68, 12, 3665-3678 (2008) · Zbl 1152.34053
[10] Zhu, G.; Meng, X.; Chen, L., The dynamics of a mutual interference age structured predator-prey model with time delay and impulsive perturbations on predators, Applied Mathematics and Computation, 216, 1, 308-316 (2010) · Zbl 1184.92059
[11] Lakshmikantham, D. B.; Simeonov, P., Theory of Impulsive Differential Equations (1989), Singapore: World Scientific Publisher, Singapore · Zbl 0719.34002
[12] Baĭnov, D.; Simeonov, P., Impulsive Differential Equations: Periodic Solutions and Applications, 66 (1993), Harlow, UK: Longman, Harlow, UK · Zbl 0815.34001
[13] Benchohra, M.; Henderson, J.; Ntouyas, S., Impulsive Differential Equations and Inclusions, 2 (2006), New York, NY, USA: Hindawi Publishing Corporation, New York, NY, USA · Zbl 1130.34003
[14] Liu, Z. J., Positive periodic solutions for a delay multispecies logarithmic population model, Chinese Journal of Engineering Mathematics, 19, 4, 11-16 (2002) · Zbl 1041.34059
[15] Lu, S.; Ge, W., Existence of positive periodic solutions for neutral logarithmic population model with multiple delays, Journal of Computational and Applied Mathematics, 166, 2, 371-383 (2004) · Zbl 1061.34053
[16] Chen, F., Periodic solutions and almost periodic solutions for a delay multispecies logarithmic population model, Applied Mathematics and Computation, 171, 2, 760-770 (2005) · Zbl 1089.92038
[17] Chen, F., Periodic solutions and almost periodic solutions of a neutral multispecies logarithmic population model, Applied Mathematics and Computation, 176, 2, 431-441 (2006) · Zbl 1089.92039
[18] Zhao, W., New results of existence and stability of periodic solution for a delay multispecies Logarithmic population model, Nonlinear Analysis: Real World Applications, 10, 1, 544-553 (2009) · Zbl 1154.34366
[19] Wang, Q.; Wang, Y.; Dai, B., Existence and uniqueness of positive periodic solutions for a neutral logarithmic population model, Applied Mathematics and Computation, 213, 1, 137-147 (2009) · Zbl 1177.34093
[20] Luo, Y.; Luo, Z., Existence of positive periodic solutions for neutral multi-delay logarithmic population model, Applied Mathematics and Computation, 216, 4, 1310-1315 (2010) · Zbl 1303.92101
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