Delayed feedback and multiple attractors in a host-parasitoid system

Journal of Mathematical Biology

Volumn 38, Issue 4, 1999, Pages 317-345

  Briggs, Cheryl J ^a   Nisbet, Roger M ^b   Murdoch, William W ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Age structure; Delayed feedback; Multiple attractors; Parasitoid; Population cycles

Indexed keywords

EID: 0009449546     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850050151     Document Type: Article

References (12)

1. W. W. Murdoch, C. J. Briggs, and R. M. Nisbet. Dynamical effects of host size- and parasitoid state- dependent attacks by parasitoids. J. Anim. Ecol., 66: 542-556, 1997
2. W. W. Murdoch, R. M. Nisbet, S. P. Blythe, W. S. C. Gurney, and J. D. Reeve. An invulnerable age class and stability in delay-differential parasitoid-host models. Am. Nat., 129: 263-282, 1987
3. H. C. J. Godfray and M. P. Hassell. Natural enemies can cause discrete generations in tropical environments. Nature, 327: 144-147, 1987
4. H. C. J. Godfray and M. P. Hassell. Discrete and continuous insect populations in tropical environments. J. Anim. Ecol., 58: 153-174, 1989
5. D. M. Gordon, R. M. Nisbet, A. M. de Roos, W. S. C. Gurney, and R. K. Stewart. Discrete generations in host-parasitoid models with contrasting life cycles. J. Anim. Ecol., 60: 295-308, 1991
6. W. W. Murdoch, R. M. Nisbet, R. F. Luck, H. C. J. Godfray, and W. S. C. Gurney. Size-selective sex-allocation and host feeding in a parasitoid-host model. J. Anim. Ecol., 61: 533-541, 1992
7. A. Hastings. Cycles in cannibalistic egg-larval interactions. J. Math. Biol., 24: 651-666, 1987
8. A. Hastings and R. F. Costantino. Cannibalistic egg-larva interactions in Tribolium: An explanation for the oscillations in populations numbers. Am. Nat., 130: 36-52, 1987
9. A. M. de Roos, O. Diekmann, and J. A. J. Metz. Studying the dynamics of structured population models: A versatile technique and its application to daphnia. Am. Nat., 139: 123-147, 1992
10. A. M. de Roos. A gentle introduction to physiologically structured population models. In S. Tuljapurkar and H. Caswell, editors, Structured-population models in marine, terrestrial, and freshwater systems, pp. 119-204. Champman and Hall, New York, 1997
11. R. M. Nisbet. Delay-differential equations for structured populations. In S. Tuljapurkar and H. Caswell, editors, Structured-population models in marine, terrestrial, and freshwater systems, pages 89-118. Chapman and Hall, New York, 1997
12. O. Diekmann and S. A. van Gils. Invariant manifolds for Volterra integral equations of convolution type. J. Diff. Equa., 54: 139-180, 1984