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

Jean-Luc Boulnois
Mar 2023
摘要
The classical Lotka-Volterra predator-prey system is often used in speciescompetition modeling. An exact, closed-form solution is derived when thenatural growth rate of the prey species and decay rate of the predators areequal in magnitude. A standard functional transformation yields a novel systemof two partially uncoupled rst-order ODEs for \hybrid-species", with one beingautonomous. New exact, closed-form time-dependent solutions are derived foreach individual species. An analytical expression for the system's oscillationperiod valid for any value of the system's energy is derived in terms of anovel universal function.
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