A model of trophodynamics

Nonlinear Analysis, Theory, Methods and Applications

Volumn 35, Issue 1, 1999, Pages 37-57

  Lackey, Brad ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Method of equivalence; Second order differential equations; Trophodynamics

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; ORDINARY DIFFERENTIAL EQUATIONS; THEOREM PROVING;

SECOND ORDER DIFFERENTIAL EQUATIONS; TROPHODYNAMICS;

MATHEMATICAL MODELS;

EID: 0032763230     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00097-2     Document Type: Article

References (25)

1. P.L. Antonelli, Mathematical Essays on Growth and the Emergence of Form, Section 2D, Univ. Alberta Press, 1985.
2. P.L. Antonelli, P. Auger, R. Bradbury, Corals and starfish waves on the great barrier reef: analytical trophodynamics and 2-patch aggregation methods, Nonlinear Times and Digest 2 (1995) 261-289, or Math. Comput. Modelling, Special issue on Aggregation Methods in Population Dynamics, to appear.
3. P.L. Antonelli, P. Auger, R. Bradbury, Corals and starfish waves on the great barrier reef: analytical trophodynamics and 2-patch aggregation methods, Nonlinear Times and Digest 2 (1995) 261-289, or Math. Comput. Modelling, Special issue on Aggregation Methods in Population Dynamics, to appear.
4. P.L. Antonelli, R.H. Bradbury, Volterra-Hamilton Models in the Ecology and Evolution of Colonial Organisms, World Scientific, Singapore, 1996.
5. P.L. Antonelli, R.S. Ingarden, M. Matsumoto, The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, D. Reidel and Kluwer Academic Press, 1993.
6. W.L. Burke, Applied Differential Geometry, Cambridge, 1985.
7. É. Cartan, Observations sur le mémoir précédent, Math. Zeitschrift 37 (1933) 619-622.
8. É. Cartan, Les sous-groupes des groupes continus de transformations, Ann. de l'École Normale (1908) 57-194.
9. S.S. Chern, Sur la géometrie d'un système d'equations deifferentialles du second ordre, Bull. Sci. Math. 63 (1939) 206-212.
10. H. Flanders, Differential Forms with Applications to the Physical Sciences, Dover, New York, 1989.
11. R.B. Gardner, The Method of Equivalence and Its Applications, CBMS 58, SIAM, Philadelphia, PA, 1989.
12. J.B. Harborne, Introduction to Ecological Biochemistry, Academic Press, New York, 1988.
13. D.D. Kosambi, Parallelism and Path-Spaces, Math. Zietschrift 37 (1933) 608-618.
14. D.D. Kosambi, Systems of differential equations of the second order, Quart. J. Math. (Oxford) 6 (1935) 1-12.
15. D.S. Mulyk, Allelochemically-based interspecific interactions, Math. Comput. Modelling 13 (6) (1990), In: P.L. Antonelli (Ed.), Special issue on Proc. Internat. Workshop on Population Dynamics of Outbreaks, 1990, pp. 31-34.
16. P.J. Olver, Equivalence, Invariants, and Symmetry, Cambridge, 1995.
17. R. Pratt, Studies on Chlorella vulgaris, V, Some properties of the growth inhibitor formed by Chlorella cells, Amer J. Bot. 27 (1940) 52-56.
18. R. Pratt, Studies on Chlorella vulgaris, IX, Influence on the growth of Chlorella of continuous removal of chlorellin form the solution, Amer J. Bot. 31 (1944) 418-421.
19. R. Pratt, Studies on Chlorella vulgaris, XI, Relation between surface tension and accumulation of chlorellin, Amer J. Bot. 35 (1948) 634-637.
20. D.F. Rhoades, Evolution of plant chemical defense against herbivores, In: G.A. Rosenthal, D.H. Janzen (Ed.), Herbivores, Their Interaction with Secondary Plant Metabolites, Academic Press, New York, 1979, pp. 3-54.
21. E.L. Rice, Allelopathy, Second Edition, Academic Press, 1984.
22. G.A. Rosenthal, D.H. Janzen, Herbivores, Their Interaction with Secondary Plant Metabolites, Academic Press, New York, 1979.
23. D.H. Sattinger, O.L. Weaver, Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics, Springer, Berlin, 1986.
24. M. Spivak, Calculus on Manifolds, W.A. Benjamin, New York, 1965.
25. F.M. Williams, Dynamics of microbial populations, Systems Anal. Simulation Ecology I (1971) 197-267.