Reliable computation of equilibrium states and bifurcations in ecological systems analysis

Computers and Chemical Engineering

Volumn 31, Issue 8, 2007, Pages 993-1005

  Gwaltney, C Ryan ^a   Stadtherr, Mark A ^a  

^a University of Notre Dame   (United States)

Author keywords

Bifurcations; Ecological risk assessment; Ecosystem modeling; Equilibrium states; Food chains; Nonlinear dynamics

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTATION THEORY; IMPURITIES; MATHEMATICAL MODELS; PARAMETER ESTIMATION; SYSTEMS ANALYSIS;

ECOLOGICAL RISK ASSESSMENT; ECOSYSTEM MODELING; EQUILIBRIUM STATES; FOOD CHAINS;

ECOSYSTEMS;

BIFURCATION (MATHEMATICS); COMPUTATION THEORY; ECOSYSTEMS; IMPURITIES; MATHEMATICAL MODELS; PARAMETER ESTIMATION; SYSTEMS ANALYSIS;

EID: 34248168631     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compchemeng.2006.10.011     Document Type: Article

References (41)

1. Bartell S., Gardner R., and O'Neill R. Ecological risk estimation (1992), Lewis Publishers, Ann Arbor, MI
2. Bartell S., Lefebvre G., Kaminski G., Carreau M., and Campbell K.R. An ecosystem model for assessing ecological risks in Quebec rivers, lakes, and reservoirs. Ecological Modelling 124 (1999) 43-67
3. Bartell S., Pastorok R., Akcakaya H.R., Regan H., Ferson S., and Mackay C. Realism and relevance of ecological models used in chemical risk assessment. Human and Ecological Risk Assessment 9 (2003) 907-938
4. Bernot R.J., Brueseke M.A., Evans-White M.A., and Lamberti G.A. Acute and chronic toxicity of imidazolium-based ionic liquids on Daphnia magna. Environmental Toxicology and Chemistry 24 (2005) 87-92
5. Bernot R.J., Kennedy E.E., and Lamberti G.A. Effects of ionic liquids on the survival, movement, and feeding behavior of the freshwater snail, Physa acuta. Environmental Toxicology and Chemistry 24 (2005) 1759-1765
6. Bischof C.H., Lang B., Marquardt W., and Mönnigmann M. Verified determination of singularities in chemical processes. Proceedings of SCAN 2000, the 9th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics. Karlsruhe, Germany, September 18-22, 2000 (2000)
7. Boer M.P., Kooi B.W., and Kooijman S.A.L.M. Food chain dynamics in the chemostat. Mathematical Biosciences 150 (1998) 43-62
8. Brennecke J.F., and Maginn E.J. Ionic liquids: Innovative fluids for chemical processing. AIChE Journal 47 (2001) 2384-2389
9. Dhooge A., Govaerts W., and Kuznetsov Y.A. MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs. ACM Transactions on Mathematical Software 29 (2003) 141-164
10. Docherty K.M., and Kulpa C.F. Toxicity and antimicrobial activity of imidazolium and pyridinium ionic liquids. Green Chemistry 7 (2005) 185-189
11. Doedel, E. J., Paffenroth, R. C., Champneys, A. R., Fairgrieve, T. F., Kuznetsov, Y. A., Oldeman, B. E., et al. (2002). AUTO 2000: Continuation and bifurcation software for ordinary differential equations (with HomCont). User's Guide. Available with software at: http://sourceforge.net/projects/auto2000.
12. El-Sheikh M.M.A., and Mahrouf S.A.A. Stability and bifurcation of a simple food chain in a chemostat with removal rates. Chaos, Solitons and Fractals 23 (2005) 1475-1489
13. Fussmann G.F., Ellner S.P., Shertzer K.W., and Hairston N.G. Crossing the Hopf bifurcation in a live predator-prey system. Science 290 (2000) 1358-1360
14. Gau C.-Y., and Stadtherr M.A. New interval methodologies for reliable chemical process modeling. Computers and Chemical Engineering 26 (2002) 827-840
15. Gehrke V., and Marquardt W. A singularity theory approach to the study of reactive distillation. Computers and Chemical Engineering 21 Suppl. (1997) S1001-S1006
16. Gorman-Lewis D.J., and Fein J.B. Experimental study of the adsorption of an ionic liquid onto bacterial and mineral surfaces. Environmental Science and Technology 38 (2004) 2491-2495
17. Govaerts W.J.F. Numerical methods for bifurcations of dynamical equilibria (2000), SIAM, Philadelphia
18. Gragnani A., De Feo O., and Rinaldi S. Food chains in the chemostat: Relationships between mean yield and complex dynamics. Bulletin of Mathematical Biology 60 (1998) 703-719
19. Gwaltney C.R., Styczynski M.P., and Stadtherr M.A. Reliable computation of equilibrium states and bifurcations in food chain models. Computers and Chemical Engineering 28 (2004) 1981-1996
20. Hansen E.R., and Walster G.W. Global optimization using interval analysis (2004), Marcel Dekker, New York
21. Jaulin L., Kieffer M., Didrit O., and Walter E. Applied interval analysis (2001), Springer-Verlag, London
22. Kearfott R.B. Rigorous global search: Continuous problems (1996), Kluwer, Dordrecht, The Netherlands
23. Kooi B.W. Numerical bifurcation analysis of ecosystems in a spatially homogeneous environment. Acta Biotheoretica 51 (2003) 189-222
24. Kooi B.W., Boer M.P., and Kooijman S.A.L.M. Complex dynamic behavior of autonomous microbial food chains. Journal of Mathematical Biology 36 (1997) 24-40
25. Kuznetsov Y.A. Elements of applied bifurcation theory (1998), Springer-Verlag, New York
26. Lu H., Axe L., and Tyson T. Development and application of computer simulation tools for ecological risk assessment. Environmental Modeling and Assessment 8 (2003) 311-322
27. Makino K., and Berz M. Taylor models and other validated functional inclusion methods. International Journal of Pure and Applied Mathematics 4 (2003) 379-456
28. Moghadas S.M., and Gumel A.B. Dynamical and numerical analysis of a generalized food-chain model. Applied Mathematics and Computation 142 (2003) 35-49
29. Mönnigmann M., and Marquardt W. Normal vectors on manifolds of critical points for parametric robustness of equilibrium solutions of ODE systems. Journal of Nonlinear Science 12 (2002) 85-112
30. Moore R.E. Interval analysis (1996), Prentice-Hall, Englewood Cliffs, NJ
31. Naito W., Miyamoto K., Nakanishi J., Masunaga S., and Bartell S. Application of an ecosystem model for aquatic ecological risk assessment of chemicals for a Japanese lake. Water Research 36 (2002) 1-14
32. Naito W., Miyamoto K., Nakanishi J., Masunaga S., and Bartell S. Evaluation of an ecosystem model in ecological risk assessment of chemicals. Chemosphere 53 (2003) 363-375
33. Neumaier A. Interval methods for systems of equations (1990), Cambridge University Press, Cambridge, UK
34. Pastorok R. Introduction: Improving chemical risk assessments through ecological modeling. Human and Ecological Risk Assessment 9 4 (2003) 885-888
35. Pastorok R., Akcakaya H.R., Regan H., Ferson S., and Bartell S. Role of ecological modeling in risk assessment. Human and Ecological Risk Assessment 9 4 (2003) 939-972
36. Pernak J., Sobaszkiewicz K., and Mirska I. Anti-microbial activities of ionic liquids. Green Chemistry 5 (2003) 52-56
37. Ranke J., Molter K., Stock F., Bottin-Weber U., Poczobutt J., Hoffmann J., et al. Biological effects of imidazolium ionic liquids with varying chain lengths in acute Vibrio fischeri and WST-1 cell viability assays. Ecotoxicology and Environmental Safety 58 (2004) 396-404
38. Ropel L., Belvèze L.S., Aki S.N.V.K., Stadtherr M.A., and Brennecke J. Octanol-water partition coeffcients of imidazolium-based ionic liquids. Green Chemistry 7 (2005) 83-90
39. Schnepper C.A., and Stadtherr M.A. Robust process simulation using interval methods. Computers and Chemical Engineering 20 (1996) 187-199
40. Seydel R. From equilibrium to chaos: Practical bifurcation and stability analysis (1988), Elsevier, New York, NY
41. Stepnowski P., Skladanowski A.C., Ludwiczak A., and Laczynska E. Evaluating the cytotoxicity of ionic liquids using human cell line HeLa. Human and Experimental Toxicology 23 (2004) 513-517