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

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.

16 pages, 7 figures, accepted in 'Physics of Plasmas'

References in corpus (3)

• Compact formulas for bounce/transit averaging in axisymmetric tokamak geometry
• Zonal profile corrugations and staircase formation: Role of the transport crossphase
• Effects of zonal flows on transport crossphase in dissipative trapped-electron mode turbulence in edge plasmas

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