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Almost periodic solution for a Volterra model with mutual interference and Beddington-DeAngelis functional response. (English) Zbl 1175.34058
The authors consider a Volterra model with mutual interference and Beddington-DeAngelis functional response. By applying the comparison theorem for differential equations and constructing a suitable Lyapunov functional, sufficient conditions for permanence and existence of a unique globally attractive positive almost periodic solution are obtained. A suitable example together with its numeric simulations is given to illustrate the feasibility of the main results.

34C27Almost and pseudo-almost periodic solutions of ODE
34D05Asymptotic stability of ODE
92D25Population dynamics (general)
[1]Wang, K.; Zhu, Y.: Global attractivity of positive periodic solution for a Volterra model, Appl. math. Comput. 203, No. 2, 493-501 (2008) · Zbl 1178.34052 · doi:10.1016/j.amc.2008.04.005
[2]Berryman, A. A.: The origins and evolution of predator – prey theory, Ecology 75, 1530-1535 (1992)
[3]Chen, F. D.: Periodicity in a nonlinear predator – prey system with state dependent delays, Acta math. Appl. sinica engl. Ser. 21, No. 1, 1-10 (2005) · Zbl 1096.34050 · doi:10.1007/s10255-005-0214-2
[4]Shen, C. X.: Permanence and global attractivity of the food-chin system with Holling IV type functional response, Appl. math. Comput. 194, No. 1, 179-185 (2007) · Zbl 1193.34142 · doi:10.1016/j.amc.2007.04.019
[5]Zhang, L.; Teng, Z. D.: Permanence for a delayed periodic predator – prey model with prey dispersal in multi-patches and predator density-independent, J. math. Anal. appl. 338, No. 1, 175-193 (2008) · Zbl 1147.34056 · doi:10.1016/j.jmaa.2007.05.016
[6]Chen, F.; Cao, X. H.: Existence of almost periodic solution in a ratio-dependent Leslie system with feedback controls, J. math. Anal. appl. 341, 1399-1412 (2008) · Zbl 1145.34026 · doi:10.1016/j.jmaa.2007.09.075
[7]Song, X. Y.; Li, Y. F.: Dynamic behaviors of the periodic predator – prey model with modified Leslie – gower Holling-type II schemes and impulsive effect, Nonlinear anal. Real world appl. 9, No. 1, 64-79 (2008) · Zbl 1142.34031 · doi:10.1016/j.nonrwa.2006.09.004
[8]Zhou, X. Y.; Shi, X. Y.; Song, X. Y.: Analysis of nonautonomous predator – prey model with nonlinear diffusion and time delay, Appl. math. Comput. 196, 129-136 (2008) · Zbl 1147.34355 · doi:10.1016/j.amc.2007.05.041
[9]Meng, X. Z.; Xu, W. J.; Chen, L. S.: Profitless delays for a nonautonomous Lotka – Volterra predator – prey almost periodic system with dispersion, Appl. math. Comput. 188, No. 1, 365-378 (2007) · Zbl 1113.92070 · doi:10.1016/j.amc.2006.09.133
[10]Liu, S. Q.; Zhang, J. H.: Coexistence and stability of predator – prey model with beddington – deangelis functional response and stage structure, J. math. Anal. appl. 342, No. 1, 446-460 (2008) · Zbl 1146.34057 · doi:10.1016/j.jmaa.2007.12.038
[11]Ding, X. Q.; Jiang, J. F.: Multiple periodic solutions in delayed gause-type ratio-dependent predator – prey systems with non-monotonic numerical responses, Math. comput. Modell. 47, No. 11, 1323-1331 (2008) · Zbl 1145.34332 · doi:10.1016/j.mcm.2007.06.025
[12]Hassel, M. P.: Density dependence in single-species population, J. anim. Ecol. 44, 283-295 (1975)
[13]Chen, L. S.: Mathematics ecology models and research methods, (1988)
[14]Fan, M.; Kuang, Y.: Dynamics of a nonautonomous predator – prey system with the beddington – deangelis functional response, J. math. Anal. appl. 259, 15-39 (2004) · Zbl 1051.34033 · doi:10.1016/j.jmaa.2004.02.038
[15]Arditi, R.; Ginzburg, L. R.: Coupling in predator – prey dynamics: ratio-dependence, J. theoret. Biol. 139, 1287-1296 (1989)
[16]Arditi, R.; Saiah, H.: Empirical evidence of the role of heterogeneity in ratio-dependent consumption, Ecology 73, 1544-1551 (1992)
[17]Gutierrez, A. P.: The physiological basis of ratio-dependent predator – prey theory: a metabolic pool model of nicholsons blowflies as an example, Ecology 73, 1552-1563 (1992)
[18]Zhou, Z. H.; Yang, Z. H.: Periodic solutions in higher-dimensional Lotka – Volterra neutral competition systems with state-dependent delays, Appl. math. Comput. 189, No. 1, 986-995 (2007) · Zbl 1134.34046 · doi:10.1016/j.amc.2006.11.174
[19]Han, F.; Wang, Q. Y.: Existence of multiple positive periodic solutions for differential equation with state-dependent delays, J. math. Anal. appl. 324, No. 2, 908-920 (2006) · Zbl 1112.34049 · doi:10.1016/j.jmaa.2005.12.050
[20]Chen, F. D.: Almost periodic solution of the non-autonomous two-species competitive model with stage structure, Appl. math. Comput. 181, 685-693 (2006) · Zbl 1163.34030 · doi:10.1016/j.amc.2006.01.055
[21]Shi, C. L.; Li, Z.; Chen, F. D.: The permanence and extinction of a nonlinear growth rate single-species non-autonomous dispersal models with time delays, Nonlinear anal. Real world appl. 8, No. 5, 536-1550 (2007) · Zbl 1128.92053 · doi:10.1016/j.nonrwa.2006.08.005
[22]Feng, C. H.; Liu, Y. J.: Almost periodic solutions for delay Lotka – Volterra competitive systems, Acta math. Appl. sinica 28, No. 3, 459-465 (2005)
[23]Feng, C. H.; Wang, P. G.: The existence of almost periodic solutions of some delay differential equations, Comput. math. Appl. 47, No. 8, 1225-1231 (2004) · Zbl 1080.34561 · doi:10.1016/S0898-1221(04)90116-2
[24]Yang, X. T.; Yuan, R.: Global attractivity and positive almost periodic solution for delay logistic differential equation, Nonlinear anal. 68, No. 1, 54-72 (2008) · Zbl 1136.34057 · doi:10.1016/j.na.2006.10.031
[25]Yang, X. T.: Global attractivity and positive almost periodic solution of a single species population model, J. math. Anal. appl. 336, No. 1, 111-126 (2007) · Zbl 1132.34050 · doi:10.1016/j.jmaa.2007.02.045
[26]Liu, S. Q.; Chen, L. S.: Permanence, extinction and balancing survival in nonautonomous system with delays, Appl. math. Comput. 129, 481-499 (2002) · Zbl 1035.34088 · doi:10.1016/S0096-3003(01)00058-3
[27]He, C. Y.: Almost periodic differential equations, (1992)
[28]A.M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, vol. 377, Springer-Verlag, Berlin, 1974. · Zbl 0325.34039
[29]Wang, Q.; Dai, B. X.: Almost periodic solution for n-species Lotka – Volterra competitive system with delay and feedback controls, Appl. math. Comput. 200, No. 1, 133-146 (2008) · Zbl 1146.93021 · doi:10.1016/j.amc.2007.10.055