Local dynamical equivalence of certain food webs

Ocean Dynamics

Volumn 59, Issue 2, 2009, Pages 417-427

  Gross, Thilo ^a   Feudel, Ulrike ^b  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^b UNIVERSITY OF OLDENBURG   (Germany)

Author keywords

Bifurcation analysis; Coarse graining; Dynamics; Food web; Model reduction; Modeling

Indexed keywords

BIFURCATION ANALYSIS; COARSE-GRAINING; FOOD WEB; MODEL REDUCTION; MODELING;

ANALYTICAL GEOCHEMISTRY; BIFURCATION (MATHEMATICS); BIOGEOCHEMISTRY; DYNAMICS; FOOD ADDITIVES; MATHEMATICAL MODELS;

ECOLOGY;

ALGORITHM; ECOSYSTEM DYNAMICS; ECOSYSTEM MODELING; FOOD WEB; MAPPING METHOD;

EID: 67349234959     PISSN: 16167341     EISSN: 16167228     Source Type: Journal    
DOI: 10.1007/s10236-008-0165-2     Document Type: Article

References (28)

1. JC Allen WM Schaffer D Rosko 1993 Chaos reduces species extinction by amplifying local population noise Nature 364 229 232 (Pubitemid 23969241)
2. TR Anderson 2005 Plankton functional type modelling: running before we can walk? J Plankton Res 27 11 1073 1081 (Pubitemid 43012740)
3. JM Cushing B Dennis RA Desharnais RF Constantino SM Henson 1998 Nonlinear population dynamics: models, experiments and data J Theor Biol 194 1 9 (Pubitemid 28456974)
4. AM Edwards A Yool 2000 The role of higher predation in plankton population models J Plankton Res 22 6 1085 1112 (Pubitemid 30392608)
5. S Ellner P Turchin 1995 Chaos in a noisy world: new methods and evidence from time-series analysis Am Nat 145 343 375
6. GF Fussmann G Heber 2002 Food web complexity and population dynamics Ecol Lett 5 394 401 (Pubitemid 34523106)
7. Gross T (2004) Population dynamics: general results from local analysis. Der Andere Verlag, Tönning
8. T Gross U Feudel 2006 Generalized models as a universal approach to the analysis of nonlinear dynamical systems Phys Rev E 73 016205 016214 (Pubitemid 43254433)
9. T Gross W Ebenhöh U Feudel 2005 Long food chains are in general chaotic Oikos 109 1 135 155 (Pubitemid 40518614)
10. Gross T, Edwards AM, Feudel U (2008) The invisible niche: weakly density-dependent mortality and the coexistence of species. Bull Math Biol (unpublished)
11. I Hanski P Turchin E Korplmakl H Henttonen 1993 Population oscillations of boreal rodents: regulation by mustelid predators leads to chaos Nature 364 232 235 (Pubitemid 23257079)
12. Kuznetsov Y (1989) Elements of applied bifurcation theory. Springer, Berlin
13. RM May 1974 Biological populations with nonoverlapping generations: stable points, stable cycles and chaos Science 186 645 647
14. RM May 1976 Simple mathematical models with very complicated dynamics Nature 261 5560 459 467
15. RM May 1987 Chaos and the dynamics of biological populations Proc R Soc Lond A 413 1844 27 44 (Pubitemid 18533680)
16. MEJ Newman M Girvan 2004 Finding and evaluating community structure in networks Phys Rev E 69 026113 026115
17. D Nychka S Ellner D McCaffrey AR Gallant 1992 Finding chaos in noisy systems J R Stat Soc B 54 2 399 426
18. S Petrovskii B Li H Malchow 2004 Transition to spatiotemporal chaos can resolve the paradox of enrichment Ecol Complex 1 37 47 (Pubitemid 40171924)
19. V Rai WM Schaffer 2001 Chaos in ecology Chaos Solitons Fractals 12 197 203
20. GD Ruxton P Rohani 1998 Population floors and persistence of chaos in population models Theor Popul Biol 53 175 183 (Pubitemid 28417965)
21. RV Solé J Bascompte J Valls 1992 Stability and complexity of spatially extended two-species competition J Theor Biol 159 469 480 (Pubitemid 23055509)
22. JH Steele EW Henderson 1992 The role of predation in plankton models J Plankton Res 14 1 157 172 (Pubitemid 23395173)
23. R Steuer T Gross R Selbig B Blasius 2006 Structural kinetic modelling of metabolic networks Proc Natl Acad Sci U S A 103 32 11868 1187 (Pubitemid 44215778)
24. R Steuer AN Nesi AR Fernie T Gross B Blasius J Selbig 2007 From structure to dynamics of metabolic pathways: application to the plant mitochondrial tca cycle Bioinformatics 23 11 1378 1385 (Pubitemid 47050520)
25. D Tilman D Wedin 1991 Oscillations and chaos in the dynamics of perennial grasses Nature 353 653 655 (Pubitemid 21912580)
26. P Turchin SP Ellner 2000 Living on the edge of chaos: population dynamics of fennoscandian voles Ecology 81 11 3099 3116
27. RK Upadhyay SRK Iyengar V Rai 1998 Chaos: an ecological reality? Int J Bifurc Chaos 8 6 1325 1333 (Pubitemid 128188053)
28. GAK van Voorn D Stiefs T Gross B Kooi U Feudel SALM Kooijman 2008 Stabilization due to predator interference: comparison of different analysis approaches Math Biosci Eng 5 567 583