Multiple attractors and boundary crises in a tri-trophic food chain

Mathematical Biosciences

Volumn 169, Issue 2, 2001, Pages 109-128

  Boer, M P ^a   Kooi, B W ^a   Kooijman, S A L M ^a  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Food chain; Global bifurcations; Heteroclinic orbits; Homoclinic orbits; Next minimum map

Indexed keywords

ECOLOGICAL MODELING; FOOD CHAIN; TRITROPHIC INTERACTION;

ARTICLE; CHAOTIC DYNAMICS; FOOD CHAIN; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; NONLINEAR SYSTEM;

ANIMALS; BIOREACTORS; FOOD CHAIN; MATHEMATICAL COMPUTING; MODELS, BIOLOGICAL; PREDATORY BEHAVIOR;

GOES;

EID: 0035109332     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(00)00058-4     Document Type: Article

References (38)

1. Nonlinear dynamics and population disappearances
2. Bifurcation structure of a three-species food chain model
3. Remarks on food chain dynamics
4. Chaos in a three-species food chain
5. Chaos in three species food chains
6. Singular homoclinic bifurcations in tri-trophic food chains
7. Food chains in the chemostat: Relationships between mean yield and complex dynamics
8. Homoclinic and heteroclinic orbits in a tri-trophic food chain
9. Complex dynamic behaviour of autonomous microbial food chains
10. Food chain dynamics in the chemostat
11. Consequences of population models for the dynamics of food chains
12. Chaotic dynamics of a food web in a chemostat
13. Invading species can stabilize simple trophic systems
14. What equilibrium behaviour of Lotka-Volterra models does not tell us about food webs
15. Crises, sudden changes in chaotic attractors, and transient chaos
16. Mathematical modeling in microbial ecology
17. Chaos and peak-to-peak dynamics in a plankton-fish model
18. Dstool: Computer assisted exploration of dynamical systems
19. Investigating torus bifurcations in the forced van der Pol oscillator
20. Elements of applied bifurcation theory
21. Transients and oscillations in continuous culture
22. Convergence results and a Poincaré-Bendixon trichotomy for asymptotically autonomous differential equations
23. Biological populations with non-overlapping generations: Stable points, stable cycles and chaos
24. Simple mathematical models with very complicated dynamics
25. Bifurcations and dynamic complexity in simple ecological models
26. A numerical toolbox for homoclinic bifurcation analysis
27. Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem
28. The numerical computation of connecting orbits in dynamical systems
29. The numerical computation of homoclinic orbits for maps
30. Some flesh on the skeleton: The bifurcations of bimodal maps
31. Interval dynamics
32. Stable orbits and bifurcation of maps of the interval