×

Global stability of almost periodic solution of multispecies mutualism system with time delays and impulsive effects. (English) Zbl 1410.34207

Summary: This paper discusses an almost periodic multispecies Lotka-Volterra mutualism system with time delays and impulsive effects. By using the theory of comparison theorem and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence and uniqueness and global asymptotical stability of almost periodic solution of this system are obtained. The results of this paper is completed new. An suitable example indicates the feasibility of the main results.

MSC:

34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D25 Population dynamics (general)
34C25 Periodic solutions to ordinary differential equations
34K13 Periodic solutions to functional-differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Xia, Yonghui; Cao, Jinde; Cheng, Sui Sun, Periodic solutions for a Lotka-Volterra mutualism system with several delays, Appl. Math. Modell., 31, 1960-1969, (2007) · Zbl 1167.34343
[2] Li, Yongkun; Zhang, Hongtao, Existence of periodic solutions for a periodic mutualism model on time scales, J. Math. Anal. Appl., 343, 818-825, (2008) · Zbl 1146.34326
[3] Wang, Yuan-Ming, Asymptotic behavior of solutions for a Lotka-Volterra mutualism reaction-diffusion system with time delays, Comput. Math. Appl., 58, 597-604, (2009) · Zbl 1189.35157
[4] Wang, Changyou; Wang, Sh.u.; Yang, Fuping; Li, Linrui, Global asymptotic stability of positive equilibrium of three-species Lotka-Volterra mutualism models with diffusion and delay effects, Appl. Math. Modell., 34, 4278-4288, (2010) · Zbl 1201.35030
[5] Liu, Meng; Wang, Ke, Analysis of a stochastic autonomous mutualism model, J. Math. Anal. Appl., 402, 392-403, (2013) · Zbl 1417.92141
[6] Li, Y., Positive periodic solutions of a discrete mutualism model with time delays, Int. J. Math. Math. Sci., 4, 499-506, (2005) · Zbl 1081.92042
[7] Chen, Fengde, Permanence for the discrete mutualism model with time delay, Math. Comput. Modell., 47, 431-435, (2008) · Zbl 1148.39017
[8] Li, Yongkun; Zhang, Hongtao, Existence of periodic solutions for a periodic mutualism model on time scales, J. Math. Anal. Appl., 343, 818-825, (2008) · Zbl 1146.34326
[9] Wang, Yijie, Periodic and almost periodic solutions of a nonlinear single species discrete model with feedback control, Appl. Math. Comput., 219, 5480-5496, (2013) · Zbl 1280.92055
[10] Zhang, Tianwei; Gan, Xiaorong, Almost periodic solutions for a discrete fishing model with feedback control and time delays, Commun. Nonlinear Sci. Numer. Simul., 18, (2013) · Zbl 1287.39005
[11] Wang, Yijie, Periodic and almost periodic solutions of a nonlinear single species discrete model with feedback control, Appl. Math. Comput., 219, 5480-5486, (2013) · Zbl 1280.92055
[12] Zengji, Du.; Lv, Yansen, Permanence and almost periodic solution of a Lotka-Volterra model with mutual interference and time delays, Appl. Math. Modell., 37, 1054-1068, (2013) · Zbl 1351.34080
[13] Wang, Li; Mei, Yu.; Niu, Pengcheng, Periodic solution and almost periodic solution of impulsive lasota-wazewska model with multiple time-varying delays, Comput. Math. Appl., 64, 2383-2394, (2012) · Zbl 1268.34129
[14] Yang, Bixiang; Li, Jianli, An almost periodic solution for an impulsive two-species logarithmic population model with time-varying delay, Math. Comput. Modell., 55, 1963-1968, (2012) · Zbl 1255.34070
[15] Zhang, Tianwei; Li, Yongkun; Ye, Yuan, On the existence and stability of a unique almost periodic solution of schoener’s competition model with pure-delays and impulsive effects, Commun. Nonlinear Sci. Numer. Simul., 17, 1408-1422, (2012) · Zbl 1256.34074
[16] Yang, Bixiang; Li, Jianli, An almost periodic solution for an impulsive two-species logarithmic population model with time-varying delay, Math. Comput. Modell., 55, 1963-1968, (2012) · Zbl 1255.34070
[17] Li, Y. K.; Zhang, T. W., Existence of almost periodic solutions for Hopfield neural networks with continuously distributed delays and impulses, Electron. J. Differ. Equ., 2009, 152, 1-8, (2009) · Zbl 1186.34094
[18] Li, Y. K.; Zhang, T. W., Global exponential stability of fuzzy interval delayed neural networks with impulses on time scales, Int. J. Neural Syst., 19, 6, 449-456, (2009)
[19] Zhou, J. W.; Li, Y. K., Existence and multiplicity of solutions for some Dirichlet problems with impulsive effects, Nonlinear Anal., 71, 2856-2865, (2009) · Zbl 1175.34035
[20] Li, Y. K.; Zhang, T. W., Existence and uniqueness of anti-periodic solution for a kind of forced Rayleigh equation with state dependent delay and impulses, Commun. Nonlinear Sci. Numer. Simul., 15, 4076-4083, (2010) · Zbl 1222.34096
[21] Li, Y. K.; Zhang, T. W.; Xing, Z. W., The existence of nonzero almost periodic solution for Cohen-Grossberg neural networks with continuously distributed delays and impulses, Neurocomputing, 73, 3105-3113, (2010)
[22] Long, Fei, Positive almost periodic solution for a class of nicholsons blowflies model with a linear harvesting term, Nonlinear Anal.: Real World Appl., 13, 686-693, (2012) · Zbl 1238.34131
[23] Lin, Xiaojie; Zengji, Du.; Lv, Yansen, Global asymptotic stability of almost periodic solution for a multispecies competition-predator system with time delays, Appl. Math. Comput., 219, 4908-4923, (2013) · Zbl 1418.37132
[24] Liu, Xingguo; Meng, Junxia, The positive almost periodic solution for Nicholson-type delay systems with linear harvesting terms, Appl. Math. Modell., 36, 3289-3298, (2012) · Zbl 1252.34082
[25] Ding, Huisheng; Nieto, Juan J., A new approach for positive almost periodic solutions to a class of nicholson’s blowflies model, J. Comput. Appl. Math., 253, 249-254, (2013) · Zbl 1288.92017
[26] Zengji, Du.; Lv, Yansen, Permanence and almost periodic solution of a Lotka-Volterra model with mutual interference and time delays, Appl. Math. Modell., 37, 1054-1068, (2013) · Zbl 1351.34080
[27] Wang, Lijuan, Almost periodic solution for nicholson’s blowflies model with patch structure and linear harvesting terms, Appl. Math. Modell., 37, 2153-2165, (2013) · Zbl 1349.34288
[28] Nakata, Y.; Muroya, Y., Permanence for nonautonomous Lotka-Volterra cooperative systems with delays, Nonlinear Anal: RWA, 11, 528-534, (2010) · Zbl 1186.34119
[29] Zheng, Z. X., Theory of functional differential equations, (1994), Anhui Education Press
[30] Wang, Q.; Dai, B., Almost periodic solution for n-species Lotka-Volterra competitive system with delay and feedback controls, Appl. Math. Comput., 200, 133-146, (2008) · Zbl 1146.93021
[31] Meng, X.; Chen, L., Almost periodic solution of non-autonomous Lotka-Volterra predator-prey dispersal system with delays, J. Theor. Biol., 243, 562-574, (2006)
[32] Shi, C.; Li, Z.; Chen, F., The permanence and extinction of a nonlinear growth rate single-species non-autonomous dispersal models with time delays, Nonlinear Anal. Real World Appl., 8, 1536-1550, (2007) · Zbl 1128.92053
[33] Chen, F., Almost periodic solution of the non-autonomous two-species competitive model with stage structure, Appl. Math. Comput., 181, 685-693, (2006) · Zbl 1163.34030
[34] Wang, Q.; Dai, B., Almost periodic solution for n-species Lotka-Volterra competitive system with delay and feedback controls, Appl. Math. Comput., 200, 133-146, (2008) · Zbl 1146.93021
[35] Bohr, H., Almost periodic functions, (1947), Chelsea New York, NY, USA
[36] Fink, A. M., Almost periodic differential equations, Lecture Notes in Mathematics, vol. 377, (1974), Springer-Verlag Berlin · Zbl 0325.34039
[37] Shen, C., Permanence and global attractivity of the food-chin system with Holling IV type functional response, Appl. Math. Comput., 194, 179-185, (2007) · Zbl 1193.34142
[38] Zeng, G.; Chen, L.; Sun, L.; Liu, Y., Permanence and the existence of the periodic solution of the non-autonomous two-species competitive model with stage structure, Adv. Complex Syst., 7, 385-393, (2004) · Zbl 1080.34037
[39] Barbalat, I., System dequations differentielles doscillations nonlinears, Rev. Roumaine Math. Pures Appl., 4, 267-270, (1959) · Zbl 0090.06601
[40] Samoilenko, A. M.; Perestyuk, N. A., Differential equations with impulse effect, (1995), World Scientific Singapore · Zbl 0837.34003
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.