The Wagner Theory of 2-Dimensional Constant Sprays and its Applications in Evolutionary Biology
- 1 March 2003
- journal article
- research article
- Published by World Scientific Pub Co Pte Ltd in Open Systems & Information Dynamics
- Vol. 10 (01), 65-87
- https://doi.org/10.1023/a:1022975309215
Abstract
The present work draws on classical projective geometry of general path spaces to further study biologically motivated models in the theory of Volterra-Hamilton systems with constant coefficients. In particular, it is shown here that 2-species systems of competitive, parasitic or mutualistic type are all projectively flat (time-sequencing equivalent) and unstable. Yet, they possess first integrals of the motion. Proofs are from Wagner theory, which is in essence, just the 2-dimensional Finsler geometry of semi-symmetric connections.Keywords
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