Liu, Xia; Xing, Yepeng Bifurcations of a ratio-dependent Holling-Tanner system with refuge and constant harvesting. (English) Zbl 1272.92042 Abstr. Appl. Anal. 2013, Article ID 478315, 10 p. (2013). Summary: The bifurcation properties of a predator prey system with refuge and constant harvesting are investigated. The number of the equilibria and the properties of the system will change due to refuge and harvesting, which leads to the occurrence of several kinds bifurcation phenomena, for example, the saddle-node bifurcation, Bogdanov-Takens bifurcation, Hopf bifurcation, backward bifurcation, separatrix connecting a saddle-node and a saddle bifurcation and heteroclinic bifurcation, and so forth. Our main results reveal much richer dynamics of the system compared to the system with no refuge and harvesting. Cited in 3 Documents MSC: 92D25 Population dynamics (general) 34C23 Bifurcation theory for ordinary differential equations 37N25 Dynamical systems in biology × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Liang, Z.; Pan, H., Qualitative analysis of a ratio-dependent Holling-Tanner model, Journal of Mathematical Analysis and Applications, 334, 2, 954-964 (2007) · Zbl 1124.34030 · doi:10.1016/j.jmaa.2006.12.079 [2] Rebaza, J., Dynamics of prey threshold harvesting and refuge, Journal of Computational and Applied Mathematics, 236, 7, 1743-1752 (2012) · Zbl 1235.92048 · doi:10.1016/j.cam.2011.10.005 [3] Gupta, R. P.; Chandra, P., Bifurcation analysis of modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting, Journal of Mathematical Analysis and Applications, 398, 1, 278-295 (2013) · Zbl 1259.34035 · doi:10.1016/j.jmaa.2012.08.057 [4] Liu, X.; Han, M., Chaos and Hopf bifurcation analysis for a two species predator-prey system with prey refuge and diffusion, Nonlinear Analysis, 12, 2, 1047-1061 (2011) · Zbl 1222.34099 · doi:10.1016/j.nonrwa.2010.08.027 [5] Ma, Z.; Li, W.; Zhao, Y.; Wang, W.; Zhang, H.; Li, Z., Effects of prey refuges on a predator-prey model with a class of functional responses: the role of refuges, Mathematical Biosciences, 218, 2, 73-79 (2009) · Zbl 1160.92043 · doi:10.1016/j.mbs.2008.12.008 [6] Chen, L.; Chen, F.; Chen, L., Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a constant prey refuge, Nonlinear Analysis, 11, 1, 246-252 (2010) · Zbl 1186.34062 · doi:10.1016/j.nonrwa.2008.10.056 [7] Xiao, D.; Jennings, L. S., Bifurcations of a ratio-dependent predator-prey system with constant rate harvesting, SIAM Journal on Applied Mathematics, 65, 3, 737-753 (2005) · Zbl 1094.34024 · doi:10.1137/S0036139903428719 [8] Xiao, D.; Li, W.; Han, M., Dynamics in a ratio-dependent predator-prey model with predator harvesting, Journal of Mathematical Analysis and Applications, 324, 1, 14-29 (2006) · Zbl 1122.34035 · doi:10.1016/j.jmaa.2005.11.048 [9] Wang, L.-L.; Fan, Y.-H.; Li, W.-T., Multiple bifurcations in a predator-prey system with monotonic functional response, Applied Mathematics and Computation, 172, 2, 1103-1120 (2006) · Zbl 1102.34031 · doi:10.1016/j.amc.2005.03.010 [10] Tao, Y.; Wang, X.; Song, X., Effect of prey refuge on a harvested predator-prey model with generalized functional response, Communications in Nonlinear Science and Numerical Simulation, 16, 2, 1052-1059 (2011) · Zbl 1221.34149 · doi:10.1016/j.cnsns.2010.05.026 [11] Berezovskaya, F. S.; Song, B.; Castillo-Chavez, C., Role of prey dispersal and refuges on predator-prey dynamics, SIAM Journal on Applied Mathematics, 70, 6, 1821-1839 (2010) · Zbl 1242.92056 · doi:10.1137/080730603 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.