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In this work, the time-dependent solution for the Lotka-VolterraPredator-Prey model is derived with the help of the Lambert W function. Thisallows an exact analytical expression for the period of the associatedlimit-cycle oscillations (LCO), and also for the response time between predatorand prey population. These results are applied to the predator-prey interactionof zonal density corrugations and turbulent particle flux in gyrokineticsimulations of collisionless trapped-electron model (CTEM) turbulence. In theturbulence simulations, the response time is shown to increase when approachingthe linear threshold, and the same trend is observed in the Lotka-Volterramodel.

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