Limit Cycle Oscillations, response time and the time-dependent solution to the Lotka-Volterra Predator-Prey model

TL;DR

This paper derives an exact analytical solution for the Lotka-Volterra predator-prey model using Lambert W function, providing insights into limit-cycle oscillations and response times, with applications to plasma turbulence simulations.

Contribution

It introduces an exact analytical expression for the period and response time in the Lotka-Volterra model using Lambert W function, linking it to turbulence behavior.

Findings

Response time increases near the linear threshold in turbulence simulations.

Analytical expressions match numerical simulations for predator-prey oscillations.

The approach connects ecological models with plasma turbulence dynamics.

Abstract

In this work, the time-dependent solution for the Lotka-Volterra Predator-Prey model is derived with the help of the Lambert W function. This allows an exact analytical expression for the period of the associated limit-cycle oscillations (LCO), and also for the response time between predator and prey population. These results are applied to the predator-prey interaction of zonal density corrugations and turbulent particle flux in gyrokinetic simulations of collisionless trapped-electron model (CTEM) turbulence. In the turbulence simulations, the response time is shown to increase when approaching the linear threshold, and the same trend is observed in the Lotka-Volterra model.