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arXiv · 2110.11557

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

M. Leconte·P. Masson·Lei Qi
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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.

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M. Leconte, P. Masson, Lei Qi. 2021-10-22. Limit Cycle Oscillations, response time and the time-dependent solution to the Lotka-Volterra Predator-Prey model. https://doi.org/10.1063/5.0076085

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