Oscillations

Oscillations occur when biological quantities rise and fall repeatedly through time.

Sources of oscillation

Oscillations can result from predator–prey feedback, delayed regulation, seasonal forcing, biochemical feedback loops or internal nonlinear dynamics.

Damped oscillations

If trajectories spiral toward an equilibrium, the oscillations decrease in amplitude with time. This commonly occurs when the Jacobian has complex eigenvalues with negative real part.

Sustained oscillations

Some nonlinear systems possess persistent periodic motion rather than convergence to an equilibrium. These are associated with closed periodic trajectories such as limit cycles.

Quantities of interest

Oscillations are often described by amplitude, period and frequency.