Coupled Dynamics: the Lotka–Volterra Model
Two populations, each with a simple rule of its own, produce a cycle that neither population produces alone. The oscillation is a property of the coupling, not of either species.
dx/dt = αx − βxy (prey)
dy/dt = δxy − γy (predator)
Period
–
time units per cycle
Time series
Three full cycles are shown, so the window rescales when the period changes.
Phase plane
Click anywhere in the plot to start the system from a different pair of population sizes.
Dashed lines = nullclines