참고문헌
- F. Scudo and J. Ziegler, The Golden Age of Theoretical Ecology : 1923-1940, Springer-Verlag, New York, 1978.
- A.G. MacKendrick, Applications of mathematics to medical problems, Proceedings of Edinberg Mathematical Society 44(1926), 98-130.
- L. Nielsen, Effect of walleye predation on juvenile mortality and recruitment of yellow perch in oneida lake. Canadian Journal of Fish and Aquatic Science 37(1980), 11-19. https://doi.org/10.1139/f80-002
- D. Mech, The wolves of Isle Royale, U.S. Govt. Printing Office, 1966.
- G.E. Hutchinson, Circular casual systems in ecology, Ann. N.Y. Acad. Sci. 50(1948), 221-246.
- R.M. May, Time-delay versus stability in population models with two and three trophic levels, Ecology 54, 315-325.
- S. Blythe, R.M. Nisbet and W. Gurney, Instability and complex dynamica behaviour in population models with long time delay, Theoretical Polulation Biology 22(1982), 147-176. https://doi.org/10.1016/0040-5809(82)90040-5
- J. Cushing and M. Saleem, A predator prey model with age structure, Journal of Mathematical Biology 14(1982), 231-250. https://doi.org/10.1007/BF01832847
- A. Hasting and D. Wollkind, Age structure in predator-prey systems. i. a general model and a specific example, Theoretical Polulation Biology 21(1982), 44-56. https://doi.org/10.1016/0040-5809(82)90005-3
- A. Hasting and D. Wollkind, Age structure in predator-prey systems. ii. functional response and stability and the paradox of enrichment, Theoretical Polulation Biology 21(1982), 57-68. https://doi.org/10.1016/0040-5809(82)90006-5
- A. Hasting, Age dependent predation is not a simple process. i. contin- uous time models, Theoretical Polulation Biology 23(1983), 347-362. https://doi.org/10.1016/0040-5809(83)90023-0
- A. Hasting, Delays in recruitment at different trophic levels : Effects on stability, Journal of Mathematical Biology 21(1984), 35-44. https://doi.org/10.1007/BF00275221
- L. Nunney, The effect of long time delays in predator-prey systems, Theoretical Polulation Biology 27(1985), 202-221. https://doi.org/10.1016/0040-5809(85)90010-3
- L. Nunney, Short time delays in population models : a role in enhancing stability, Ecology 66(1985), 1849-1858. https://doi.org/10.2307/2937380
- W. Aiello and H. Freedman, A time delay model of single-species growth with stage structure, Mathematical Biosciences 101(1990), 139-153. https://doi.org/10.1016/0025-5564(90)90019-U
- W. Aiello, H. Freedman and J. Wu, Analysis of a model representing stage-structured population growth with stage-dependent time delay, SIAM Journal of Applied Mathematics 52(1992), 855-869. https://doi.org/10.1137/0152048
- W. Wang and L. Chen, A predator-prey system with stage structure for predator, Comput. Math. Appl. 33 (8)(1997), 83-91. https://doi.org/10.1016/S0898-1221(97)00056-4
- X. Zhang, L. Chen and U.A. Neumann, The stage-structured predator-prey model and optimal harvesting policy, Mathematical Biosciences 168(2000), 201-210. https://doi.org/10.1016/S0025-5564(00)00033-X
- X. Song and L. Chen, Optimal harvesting and stability for a two-species competitive system with stage structure, Mathematical Biosciences 170(2001), 173-186. https://doi.org/10.1016/S0025-5564(00)00068-7
- X. Song and L. Chen, Optimal harvesting and stability for a predator-prey system with stage structure, Acta Math. Appl. Sin. 18 (3)(2002), 423-430. https://doi.org/10.1007/s102550200042
- M. Bandyopadhyay and Sandip Banerjee, A stage-structured preypredator model with discrete time delay, Applied Mathematics and Computation 182(2006), 1385-1398. https://doi.org/10.1016/j.amc.2006.05.025
- O. Arino, E. Sanchez and A. Fathallah, State-dependent delay differential equations in population dynamics: modeling and analysis, Amer. Math. Soc., Providence, RI 29(2001), 19-36.
- R. Xu, M.A. Chaplin and F.A. Davidson, Persistence and stability of a stage-structured predator-prey model with time delays, Appl. Math. Comp. 150(2004), 259-277. https://doi.org/10.1016/S0096-3003(03)00226-1
- S.A. Gourley and Y. Kuang, A stage structured predator-prey model and its dependence on maturation delay and death rate, Journal of Mathematical Biology 49(2004), 188-200.
- M. Adimy, F. Crauste and S. Ruan, Periodic oscillations in leukopoiesis models with two delays, Journal of Theoretical Biology 242(2006), 288-299. https://doi.org/10.1016/j.jtbi.2006.02.020
- Y. Li and Y. Kuang, Periodic solutions in periodic delayed gause-type predator-prey systems, Proceedings of Dynamical Systems and Applications 3(2001), 375-382.