Dynamics of asymmetric intraguild predation with time lags in reproduction and maturation

References

• Albins, M. A., & Hixon, M. A. (2008). Invasive Indo-Pacific lionfish ( Pterois Volitans) reduce recruitment of Atlantic coral-reef fishes. Marine Ecology Progress Series, 367, 233–238. doi:10.3354/meps07620.
   Web of Science ®Google Scholar
• Beretta, E., & Kuang, Y. (2002). Geometric stability switch criteria in delay differential systems with delay dependent parameters. SIAM J. Math. Anal., 33, 1144–1165. doi:10.1137/s0036141000376086.
   Web of Science ®Google Scholar
• Bhattacharyya, J., & Pal, S. (2013). Stage-structured cannibalism with delay in maturation and harvesting of an adult predator. Journal of Biological Physics, 39, 37–65. doi:10.1007/s10867-012-9284-6.
   PubMed Web of Science ®Google Scholar
• Castillo-Chavez, C., Blower, S., Driessche, P., Kirschner, van d.D., & Yakubu, A. A. (2002). Mathematical approaches for emerging and reemerging infectious diseases: An introduction. Vol. 126 of the IMA volumes in mathematics and its applications. New York, NY: Springer.
   Google Scholar
• Dhar, J., & Jatav, K. S. (2013). Mathematical analysis of a delayed stage-structured predator-prey model with impulsive diffusion between two predators territories. Ecological Complexity, 16, 59–67. doi:10.1016/j.ecocom.2012.08.001.
   Web of Science ®Google Scholar
• Diekmann, O., Nisbet, R. M., Gurney, W. S. C., , & van d Bosch, F., (1986). Simple mathematical models for cannibalism: A critique and a new approach. Mathematical Biosciences, 78, 21–46. doi:10.1016/0025-5564(86)90029-5.
   Web of Science ®Google Scholar
• Gopalsamy, K. (1992). Stability and oscillations in delay differential equations of population dynamics. MA: Kluwer Academic Publishers.
   Google Scholar
• Goreau, T. J., & Hayes, R. (1994). Coral bleaching and ocean "hot spots". Ambio, 23, 176–180.
   Web of Science ®Google Scholar
• Gourley, S. A., & Kuang, Y. (2004). A stage structured predator-prey model and its dependence on maturation delay and death rate. Journal of Mathematical Biology, 49, 188–200. doi:10.1007/s00285-004-0278-2.
   PubMed Web of Science ®Google Scholar
• Hassard, B., Kazarinoff, N., & Wan, Y. (1981). Theory and applications of Hopf bifurcation. Cambridge (MA): Cambridge University Press.
   Google Scholar
• Hastings, A. (1987). Cycles in cannibalistic egglarval interactions. Journal of Mathematical Biology, 24, 651–666. doi:10.1007/BF00275508.
   Web of Science ®Google Scholar
• Hofbauer, J., & Sigmund, K. (1989). On the stabilizing effect of predators and competitors on ecological communities. Journal of Mathematical Biology, 27, 537–548. doi:10.1007/bf00288433.
   PubMed Web of Science ®Google Scholar
• Hare, J. A., & Whitfield, P. E. (2003). An integrated assessment of the introduction of lionfish ( Pterois volitans/miles complex) to the western Atlantic Ocean. NOAA Technical Memorandum, NOS NCCOS, 2, 1–21.
   Google Scholar
• Jiao, J., Yang, X., Cai, S., & Chen, L. (2009). Dynamical analysis of a delayed predator-prey model with impulsive diffusion between two patches. Mathematics and Computers in Simulation, 80, 522–532. doi:10.1016/j.matcom.2009.07.008.
   Web of Science ®Google Scholar
• Magnusson, K. G. (1999). Destabilizing effect of cannibalism on a structured predator-prey system. Mathematical Biosciences, 155, 61–75. doi:10.1016/S0025-5564(98)10051-2.
   PubMed Web of Science ®Google Scholar
• Martin, A., & Ruan, S. (2001). Predator-prey models with delay and prey harvesting. Journal of Mathematical Biology, 43, 247–267. doi:10.1007/s002850100095.
   PubMed Web of Science ®Google Scholar
• Morris, J. A., Akins, J. L., Barse, A., Cerino, D., Freshwater, D. W., Green, S. J., Munoz, R. C., Paris, C., & Whitefield, P. E. (2009). Biology and ecology of invasive lionfishes, pterois miles and Pterois Volitans. Gulf and Caribbean Fisheries Institute, 61, 1–6.
   Google Scholar
• Morris, J. A., Jr, Shertzer, K. W., & Rice, J. A. (2011). A stage-based matrix population model of invasive lionfish with implications for control. Biological Invasions, 13, 7–12. doi:10.1007/s10530-010-9786-8.
   Web of Science ®Google Scholar
• Morris, J.A. Jr, & Whitfield, P.E., (2009). Biology, ecology, control and management of the invasive Indo-Pacific lionfish: An updated integrated assessment. NOAA Technical Memorandum NOS-NCCOS, 99, 1–65.
   Google Scholar
• Murray, G. P. D., Stillman, R. A., Gozlan, R. E., & Britton, J. R. (2013). Experimental predictions of the functional response of a freshwater fish. Ethology, 119, 751-761. doi:10.1111/eth.12117.
   Web of Science ®Google Scholar
• Polis, G. A., Myers, C. A., & Holt, R. D. (1989). The ecology and evolution of intraguild predation: Potential competitors that eat each other. Annual Review of Ecology and Systematics, 20, 297–330. doi:10.1146/annurev.ecolsys.20.1.297.
   Google Scholar
• Ruan, S. (1993). Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling. Journal of Mathematical Biology, 31, 633–654. doi:10.1007/bf00161202.
   Web of Science ®Google Scholar
• Ruan, S., & Wei, J. (2003). On the Zeros of Transdental functions with applications to stability of delay differential equations with two delays. Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 10, 863–874.
   Google Scholar
• Rudolf, V. H. W. (2007). The interaction of cannibalism and omnivory: Consequences for communitty dynamics. Ecology, 88, 2697–2705. doi:10.1890/06-1266.1.
   PubMed Web of Science ®Google Scholar
• Rudolf, V. H. W. (2008). The impact of cannibalism in the prey on predator-prey dynamics. Ecology, 89, 3116–3127. doi:10.1890/07-0709.1.
   PubMed Web of Science ®Google Scholar
• Siekmann, I., Malchow, H., & Venturino, E. (2008). An extension of the Beretta-Kuang model of viral diseases. Mathematical Biosciences and Engineering, 5, 549–565. doi:10.3934/mbe.2008.5.549.
   PubMed Web of Science ®Google Scholar
• van den Bosch, F., Roos, A. M., & Gabriel, W. (1988). Cannibalism as a life boat mechanism. Journal of Mathematical Biology, 26, 619–633. doi:10.1007/BF00276144.
   Web of Science ®Google Scholar
• Wang, W., & Chen, L. (1997). A predator-prey system with stage structure for predator. Computers & Mathematics with Applications, 33, 83–91. doi:10.1016/S0898-1221(97)00056-4.
   Web of Science ®Google Scholar
• Zhang, X., Chen, L., & Neumann, A. U. (2000). The stage-structured predator-prey model and optimal harvesting policy. Mathematical Biosciences, 168, 201–210. doi:10.1016/s0025-5564(00)00033-x.
   PubMed Web of Science ®Google Scholar