Stage-dependent predation on prey species who possess different life histories. (English) Zbl 1515.92063
References:
| [1] | Guckenheimer, J.; Oster, G.; Ipaktchi, A., The dynamics of density dependent population models, Journal of Mathematical Biology, 4, 2, 101-147 (1977) · Zbl 0379.92016 · doi:10.1007/bf00275980 |
| [2] | Pennycuick, L., A computer model of the Oxford great tit population, Journal of Theoretical Biology, 22, 3, 381-400 (1969) · doi:10.1016/0022-5193(69)90011-3 |
| [3] | Levin, S. A.; Goodyear, C. P., Analysis of an age-structured fishery model, Journal of Mathematical Biology, 9, 3, 245-274 (1980) · Zbl 0424.92020 · doi:10.1007/bf00276028 |
| [4] | Silva, J. A. L.; Hallam, T. G., Effects of delay, truncations and density dependence in reproduction schedules on stability of nonlinear Leslie matrix models, Journal of Mathematical Biology, 31, 4, 367-395 (1993) · Zbl 0853.92019 · doi:10.1007/bf00163922 |
| [5] | Mj-lhus, E.; Wikan, A., Overcompensatory recruitment and generation delay in discrete age-structured population models, Journal of Mathematical Biology, 35, 2, 195-239 (1996) · Zbl 0865.92015 · doi:10.1007/s002850050050 |
| [6] | Davydova, N. V.; Diekmann, O.; van Gils, S., Year class coexistence or competitative exclusion for strict biennials, Journal of Mathematical Biology, 46, 2, 95-131 (2003) · Zbl 1019.92024 · doi:10.1007/s00285-002-0167-5 |
| [7] | M Cushing, J., Nonlinear semelparous Leslie models, Mathematical Biosciences and Engineering, 3, 1, 17-36 (2006) · Zbl 1089.92040 · doi:10.3934/mbe.2006.3.17 |
| [8] | Cushing, J. M.; Henson, S. M., Stable bifurcations in semelparous Leslie models, Journal of Biological Dynamics, 6, sup2, 80-102 (2012) · Zbl 1447.92335 · doi:10.1080/17513758.2012.716085 |
| [9] | Cushing, J. M.; Bourguignon, J. P.; Jeltsch, R.; Pinto, A. A.; Viana, M., On the fundamental bifurcation theorem for semelparous Leslie models, Dynamics, Games and Science (2015), Berlin, Germany: Springer International Publishing, Berlin, Germany |
| [10] | Wikan, A., An analysis of a semelparous population model with density-dependent fecundity and density-dependent survival probabilities, Journal of Applied Mathematics, 2017 (2017) · Zbl 1437.92106 · doi:10.1155/2017/8934295 |
| [11] | Behncke, H., Periodical cicadas, Journal of Mathematical Biology, 40, 5, 413-431 (2000) · Zbl 1004.92040 · doi:10.1007/s002850000024 |
| [12] | Diekmann, O.; Planqué, R., The winner takes it all: how semelparous insects can become periodical, Journal of Mathematical Biology, 80, 1-2, 283-301 (2020) · Zbl 1437.37117 · doi:10.1007/s00285-019-01362-3 |
| [13] | Neubert, M. G.; Caswell, H., Density-dependent vital rates and their population dynamic consequences, Journal of Mathematical Biology, 41, 2, 103-121 (2000) · Zbl 0956.92029 · doi:10.1007/s002850070001 |
| [14] | Kon, R.; Saito, Y.; Takeuchi, Y., Permanence of single species stage-structured models, Journal of Mathematical Biology, 48, 5, 515-528 (2004) · Zbl 1057.92043 · doi:10.1007/s00285-003-0239-1 |
| [15] | Govaerts, W.; Ghaziani, R. K., Numerical bifurcation analysis of a nonlinear stage structured cannibalism population model, Journal of Difference Equations and Applications, 12, 10, 1069-1085 (2006) · Zbl 1108.37057 · doi:10.1080/10236190600986560 |
| [16] | Costantino, R. F.; Desharnais, R. A.; Cushing, J. M.; Dennis, B., Chaotic dynamics in an insect population, Science, 275, 5298, 389-391 (1997) · Zbl 1225.37103 · doi:10.1126/science.275.5298.389 |
| [17] | Neubert, M. G.; Kot, M., The subcritical collapse of predator populations in discrete-timepredator-prey models, Mathematical Biosciences, 110, 1, 45-66 (1992) · Zbl 0747.92024 · doi:10.1016/0025-5564(92)90014-n |
| [18] | Wikan, A., From chaos to chaos. An analysis of a discrete age-structuredprey-predator model, Journal of Mathematical Biology, 43, 6, 471-500 (2001) · Zbl 0996.92031 · doi:10.1007/s002850100101 |
| [19] | Agiza, H. N.; Elabbasy, E. M.; El-Metwally, H.; Elsadany, A. A., Chaotic dynamics of a discrete prey predator model with Holling type II, Nonlinear Analysis: Real World Applications, 10, 1, 116-129 (2009) · Zbl 1154.37335 · doi:10.1016/j.nonrwa.2007.08.029 |
| [20] | Eskandari, Z.; Alidousti, J.; Avazzadeh, Z.; Tenreiro Machado, J. A., Dynamics and bifurcations of a discrete-timeprey-predator model with Allee effect on the prey population, Ecological Complexity, 48 (2021) · doi:10.1016/j.ecocom.2021.100962 |
| [21] | Rana, S. M. S.; Kulsum, U., Bifurcation analysis and chaos control in a discrete-timepredator-prey system of Leslie type with simplified Holling type IV functional response, Discrete Dynamics in Nature and Society, 2017 (2017) · Zbl 1370.92145 · doi:10.1155/2017/9705985 |
| [22] | Saeed, U.; Ali, I.; Din, Q., Neimark-Sacker bifurcation and chaos control in discrete-timepredator-prey model with parasites, Nonlinear Dynamics, 94, 4, 2527-2536 (2018) · Zbl 1422.92128 · doi:10.1007/s11071-018-4507-4 |
| [23] | Din, Q., Stability, bifurcation analysis and chaos control for a predator-prey system, Journal of Vibration and Control, 25, 3, 612-626 (2019) · doi:10.1177/1077546318790871 |
| [24] | Khan, A. Q.; Khalique, T., Neimark-Sacker bifurcation and hybrid control in a discrete-timeLotka-Volterra model, Mathematical Methods in the Applied Sciences, 43, 9, 5887-5904 (2020) · Zbl 1454.37092 · doi:10.1002/mma.6331 |
| [25] | Wikan, A., On the interplay between cannibalism and harvest in stage-structured population models, Journal of Marine Biology, 2015 (2015) · doi:10.1155/2015/580520 |
| [26] | Guckenheimer, J.; Holmes, P., Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Applied Mathematical Sciences (1990), Berlin, Germany: Springer-Verlag, Berlin, Germany |
| [27] | Wikan, A., An analysis of discrete stage-structured prey and prey-predator population models, Discrete Dynamics in Nature and Society, 2017 (2017) · Zbl 1369.92105 · doi:10.1155/2017/9475854 |
| [28] | Hastings, A., Age-dependent predation is not a simple process. II. Wolves, ungulates, and a discrete time model for predation on juveniles with a stabilizing tail, Theoretical Population Biology, 26, 2, 271-282 (1984) · Zbl 0541.92018 · doi:10.1016/0040-5809(84)90033-9 |
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.
