Pelen, Neslihan Nesliye; Güvenilir, Ayşe Feza; Kaymakçalan, Billur Behavior of the solutions for predator-prey dynamic systems with Beddington-DeAngelis type functional response on periodic time scales in shifts. (English) Zbl 1470.92257 Abstr. Appl. Anal. 2016, Article ID 1463043, 9 p. (2016). Summary: We consider two-dimensional predator-prey system with Beddington-DeAngelis type functional response on periodic time scales in shifts. For this special case we try to find under which conditions the system has \(\delta_\pm\)-periodic solution. Cited in 1 Document MSC: 92D25 Population dynamics (general) 34C25 Periodic solutions to ordinary differential equations 34C60 Qualitative investigation and simulation of ordinary differential equation models 34N05 Dynamic equations on time scales or measure chains PDF BibTeX XML Cite \textit{N. N. Pelen} et al., Abstr. Appl. Anal. 2016, Article ID 1463043, 9 p. (2016; Zbl 1470.92257) Full Text: DOI References: [1] Hilger, S., Analysis on measure chains—a unified approach to continuous and discrete calculus, Results in Mathematics, 18, 1-2, 18-56, (1990) · Zbl 0722.39001 [2] Martynyuk, A. A., Stability Theory of Solutions of Dynamic Equations on Time Scales, (2012), Kiev, Ukraine: Phoenix, Kiev, Ukraine · Zbl 1262.34002 [3] Lotka, A. J., Contribution to the theory of periodic reactions, Journal of Physical Chemistry, 14, 3, 271-274, (1910) [4] Goel, N. S.; Maitra, S. C.; Montroll, E. W., On the Volterra and Other Non-Linear Models of Interacting Populations, (1971), Academic Press [5] Berryman, A. A., The origins and evolution of predator-prey theory, Ecology, 73, 5, 1530-1535, (1992) [6] Verhulst, P. H., Notice sur la loi que la population poursuit dans son accroissement, Correspondance Mathématique et Physique, 10, 113-121, (1838) [7] Lotka, A. J., Analytical note on certain rhythmic relations in organic systems, Proceedings of the National Academy of Sciences of the United States of America, 6, 7, 410-415, (1920) [8] Lotka, A. J., Elements of Physical Biology, (1925), Williams and Wilkins · JFM 51.0416.06 [9] Holling, C. S., The components of predation as revealed by a study of small-mammal predation of the european pine sawy, Canadian Entomologist, 91, 5, 293-320, (1959) [10] Holling, C. S., Some characteristics of simple types of predation and parasitism, CAN Entertainment, 91, 385-398, (1959) [11] Jost, C.; Devulder, G.; Vucetich, J. A.; Peterson, R. O.; Arditi, R., The wolves of Isle Royale display scale-invariant satiation and ratio-dependent predation on moose, Journal of Animal Ecology, 74, 5, 809-816, (2005) [12] Bohner, M.; Fan, M.; Zhang, J., Existence of periodic solutions in predator-prey and competition dynamic systems, Nonlinear Analysis: Real World Applications, 7, 5, 1193-1204, (2006) · Zbl 1104.92057 [13] Wang, W.; Shen, J.; Nieto, J. J., Permanence and periodic solution of predator-prey system with Holling type functional response and impulses, Discrete Dynamics in Nature and Society, 2007, (2007) · Zbl 1146.37370 [14] Xu, R.; Chaplain, M. A. J.; Davidson, F. A., Periodic solutions for a predator–prey model with Holling-type functional response and time delays, Applied Mathematics and Computation, 161, 2, 637-654, (2005) · Zbl 1064.34053 [15] Fan, M.; Agarwal, S., Periodic solutions for a class of discrete time competition systems, Nonlinear Studies, 9, 3, 249-261, (2002) · Zbl 1032.39002 [16] Fan, M.; Wang, K., Periodicity in a delayed ratio-dependent predator-prey system, Journal of Mathematical Analysis and Applications, 262, 1, 179-190, (2001) · Zbl 0994.34058 [17] Fan, M.; Wang, Q., Periodic solutions of a class of nonautonomous discrete time semi-ratio-dependent predator-prey systems, Discrete and Continuous Dynamical Systems: Series B, 4, 3, 563-574, (2004) · Zbl 1114.92077 [18] Huo, H.-F., Periodic solutions for a semi-ratio-dependent predator-prey system with functional responses, Applied Mathematics Letters, 18, 3, 313-320, (2005) · Zbl 1079.34515 [19] Wang, Q.; Fan, M.; Wang, K., Dynamics of a class of nonautonomous semi-ratio-dependent predator-prey systems with functional responses, Journal of Mathematical Analysis and Applications, 278, 2, 443-471, (2003) · Zbl 1029.34042 [20] Beddington, J. R., Mutual interference between parasites or predators and its effect on searching efficency, The Journal of Animal Ecology, 44, 1, 331-340, (1975) [21] DeAngelis, D. L.; Goldstein, R. A.; ONeill, R. V., A model for tropic interaction, Ecology, 56, 4, 881-892, (1975) [22] Fan, M.; Kuang, Y., Dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response, Journal of Mathematical Analysis and Applications, 295, 1, 15-39, (2004) · Zbl 1051.34033 [23] Fang, Q.; Li, X.; Cao, M., Dynamics of a discrete predator-prey system with beddington-deangelis function response, Applied Mathematics, 3, 4, 389-394, (2012) [24] Fazly, M.; Hesaaraki, M., Periodic solutions for predator-prey systems with Beddington-DeAngelis functional response on time scales, Nonlinear Analysis. Real World Applications, 9, 3, 1224-1235, (2008) · Zbl 1145.92035 [25] Wei, C.; Chen, L., Periodic solution of prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control, Journal of Applied Mathematics, 2012, (2012) · Zbl 1263.92053 [26] Li, Y., Periodic solutions of a periodic delay predator-prey system, Proceedings of the American Mathematical Society, 127, 5, 1331-1335, (1999) · Zbl 0917.34057 [27] Liu, X.; Liu, X., Necessary and sufficient conditions for the existence of periodic solutions in a predator-prey model on time scales, Electronic Journal of Differential Equations, 2012, 199, 1-13, (2012) · Zbl 1290.34056 [28] Adivar, M., A new periodicity concept for time scales, Mathematica Slovaca, 63, 4, 817-828, (2013) · Zbl 1340.34349 [29] Cui, J.; Takeuchi, Y., Permanence, extinction and periodic solution of predator-prey system with Beddington-DeAngelis functional response, Journal of Mathematical Analysis and Applications, 317, 2, 464-474, (2006) · Zbl 1102.34033 [30] Xu, C.; Liao, M., Existence of periodic solutions in a discrete predator-prey system with Beddington-DeAngelis functional responses, International Journal of Mathematics and Mathematical Sciences, 2011, (2011) · Zbl 1237.39012 [31] Zhang, J.; Wang, J., Periodic solutions for discrete predator-prey systems with the Beddington-DeAngelis functional response, Applied Mathematics Letters, 19, 12, 1361-1366, (2006) · Zbl 1140.92325 [32] Güvenilir, A. F.; Kaymakçalan, B.; Pelen, N. N., Impulsive predator-prey dynamic systems with Beddington-DeAngelis type functional response on the unification of discrete and continuous systems, Applied Mathematics, 6, 9, 1649-1664, (2015) 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.