Fast oscillating migrations in a predator-prey model

Mathematical Models and Methods in Applied Sciences

Volumn 6, Issue 2, 1996, Pages 217-226

  Poggiale, Jean Christophe ^a   Auger, Piérre ^b  

^a UNIVERSITÉ DE BOURGOGNE   (France)

^b UNIVERSITÉ LYON 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030542367     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202596000559     Document Type: Article

References (18)

1. V. Arnold, Chapître supplémentaire sur la théorie des équations différentielles ordinaires, ed. MIR (1980).
2. P. M. Auger, Dynamics and thermodynamics in hierarchically organized systems, Applications in Physics, Biology and Economics (Pergamon Press, 1989).
3. P. M. Auger and R. Roussarie, Complex ecological models with simple dynamics: from individuals to population, Acta Biotheor. 42 (1994) 111-136.
4. J. Carr, Applications of Centre Manifolds, Applied Mathematical Sciences, Vol. 35 (Springer, 1981).
5. W. G. Cale, R. V. O'Neill and R. H. Gardner, Aggregation error in nonlinear ecological models, J. Theor. Biol. 100 (1983) 539-550.
6. N. Fenichel, Persistance and smoothness of invariant manifolds for flows, Indiana Univ. Math. J. 21 (1971) 193-226.
7. T. C. Gard, Aggregation in stochastic ecosystem models, Ecol. Modelling 44 (1988) 153-164.
8. I. Hanski, The functional response of predators: worries about scale, Trends Ecol. Evol. 6 (1991) 141-142.
9. C. S. Holling, Some characteristics of simple types of predation and parasitism, Can. Ent. 91 (1959) 385-398.
10. M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds, Lecture Notes in Mathematics, Vol. 583 (Springer, 1977).
11. Y. Iwasa, V. Andreasen and S. A. Levin, Aggregation in model ecosystems. I. perfect aggregation, Ecol. Modelling 37 (1987) 287-302.
12. Y. Iwasa, S. A. Levin and V. Andreasen, Aggregation in model ecosystems. II. approximate aggregation, IMA J. Math. Appl. Med. Biol. 6 (1989) 1-23.
13. A. Kelley, The center, center-stable, stable, center-unstable and unstable manifolds, J. Differential Equations 3 (1967) 546-570.
14. M. Mangel and W. Clark, Dynamic Modeling Behavioral Ecology (Princeton Univ. Press, 1988).
15. J. Michalski, J. C. Poggiale, R. Arditi and P. M. Auger, Feeding rates and migration in a heterogeneous environment, submitted to J. Theor. Biol.
16. J. D. Murray, Mathematical Biology Biomathematics text, Vol. 19 (Springer, 1989).
17. A. I. Neishtadt, Persistence of stability loss for dynamical bifurcations, Differentsial'nye Uravneniya 23 (1987) 2060-2067.
18. A. K. Zvonkin and M. A. Shubin, Usp. Mat. Nauk. 39 (1984) 77-127.