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An Exact Closed-Form Solution of the Lotka-Volterra Equations

Dynamical Systems 2023-03-17 v1

Abstract

The classical Lotka-Volterra predator-prey system is often used in species competition modeling. An exact, closed-form solution is derived when the natural growth rate of the prey species and decay rate of the predators are equal in magnitude. A standard functional transformation yields a novel system of two partially uncoupled rst-order ODEs for \hybrid-species", with one being autonomous. New exact, closed-form time-dependent solutions are derived for each individual species. An analytical expression for the system's oscillation period valid for any value of the system's energy is derived in terms of a novel universal function.

Keywords

Cite

@article{arxiv.2303.09317,
  title  = {An Exact Closed-Form Solution of the Lotka-Volterra Equations},
  author = {Jean-Luc Boulnois},
  journal= {arXiv preprint arXiv:2303.09317},
  year   = {2023}
}