Variables aggregation in time varying discrete systems

Acta Biotheoretica

Volumn 46, Issue 3, 1998, Pages 273-297

  Sanz, Luis ^a   Bravo De La Parra, Rafael ^b  

^a ETS Ingenieros de Telecomunicacion   (Spain)

^b UNIVERSITY OF ALCALÁ   (Spain)

Author keywords

Approximate aggregation; Cyclic environment; Population dynamics; Strong ergodicity; Time scales

Indexed keywords

EID: 0032409539     PISSN: 00015342     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1001741327984     Document Type: Conference Paper

References (28)

1. Artzrouni, M (1985). Generalized stable population theory, J. Math. Biol 21: 363-381.
2. Auger, P. and R. Roussarie. (1994). Complex ecological models with simple dynamics: From individuals to populations. Acta Biotheoretica 42: 111-136.
3. Auger P. (1989). Dynamics and Thermodynamics in Hierarchically Organized Systems, Applications in Physics, Biology and Economics. Oxford, Pergamon Press.
4. Auger, P. and E. Benoit (1993). A prey-predator model in a multipatch environment with different time scales. J. Biol. Sys. 1: 187-197.
5. Auger, P. and J.C. Poggiale (1996). Aggregation and emergence in hierarchically organized systems: population dynamics, Acta Biotheoretica 44: 301-316.
6. Berman, A. and R.J. Plemmons (1979). Nonnegative Matrices in the Mathematical Sciences. Academic Press.
7. Bravo, R., P. Auger and E. Sánchez (1995). Aggregation methods in discrete Models. J. Biol. Sys. 3:603-612.
8. Bravo de la Parra, R. and E. Sánchez (1998). Aggregation methods in population dynamics discrete models. Mathematical and Computing Modelling 27: 23-39,
9. Bravo de la Parra, R., E. Sánchez and P. Auger (1997). Time scales in density dependent discrete models. J. Biol. Sys. 5: 111-129.
10. Caswell, H. (1989). Matrix Population Models. Sunderland, Sinauer Associates Inc.
11. Charlesworth, B. (1980). Evolution in Age Structured Populations. Princetown, NJ, Cambridge University Press.
12. Cohen, J. (1979). Ergodics theorems of demography. Bull. Am. Math. Soc. 1: 275-295.
13. Gourley, R. and C. Lawrence (1977). Stable population analysis in periodic environments. Theor. Popul. Biol. 11: 49-59.
14. Horn, R. and C. Johnson (1985). Matrix Analysis. Cambridge Univ. Press.
15. Iwasa, Y., V. Andreasen and S.A. Levin (1987). Aggregation in model ecosystems. (I) Perfect aggregation. Ecol. Modelling 37: 287-302.
16. Keller, E.L. (1980). Primitivity of the product of two Leslie matrices. Bull. Math. Biol. 42: 181-189.
17. Leftkovitch, L.P. (1965). The study of population growth in organisms grouped by stages. Biometrics 21: 1-18.
18. Leslie, P.H. (1945). On the use of matrices in certain population mathematics. Biometrika 33: 183-212.
19. Logofet, D.O. (1993). Matrices and Graphs. Stability Problems in Mathematical Ecology. CRC press.
20. MacArthur, R.H. (1968). Selection for life tables in a periodic environment. Amer. Nat. 102: 381-383.
21. Sánchez, E., R. Bravo de la Parra, P. Auger (1995). Linear discrete models with different time scales. Acta Biotheoretica 43: 465-479.
22. Seneta, E. (1981). Non-Negative Matrices and Markov Chains. New York, Springer Verlag.
23. Skellam, J.G. (1967). Seasonal periodicity in theoretical population ecology. Proceedings of the 5th Berkeley Symposium in Mathematical Statistics and Probability, vol 4: 179-205. Berkeley, Univ. of California Press.
24. Stewart, G.W. and J.I-Guang Sun (1990). Matrix Perturbation Theory. Academic Press.
25. Taylor, H.M. (1985). Primitivity of the product of Leslie matrices. Bull. Math. Biol. 47: 23-34.
26. Thompson, M. (1978). Asymptotic growth and stability in populations with time dependent vital rates. Math. Biosci. 42: 267-278.
27. Tuljapurkar, S. and S. Orzack (1980). Population dynamics in variable environments. I. Long-run growth rates and extinction. Theor. Pop. Biol. 18: 314-342.
28. Tuljapurkar, S. (1985). Population dynamics in variable environments. VI. Cyclical environments. Theor. Pop. Biol. 28: 1-17.