New Results on 2-Dimesional Constant Sprays with an Application to Heterochrony

Peter Antonelli, Bin Han and Joseph Modayil


The present work draws on classical projective geometry of general path spaces to further study biological motivated models of heterochrony 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 Jacobi unstable. Yet, they possess first integrals of the motion. Proofs of this are based on 2-dimensional Finsler geometry and the theory of semi-symmetric connections. A concrete model of lichens is briefly discussed.

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