Limit cycle oscillations, response time, and the time-dependent solution to the Lotka-Volterra predator-prey model

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 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 the collisionless trapped-electron mode 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.