predator_prey_ode_period

predator_prey_ode_period, a MATLAB code which sets up and solves a pair of predator prey or Lotka-Volterra ordinary differential equations (ODE) in order to estimate the period of the limit cycle. The computation involves the Lambert W function.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

predator_prey_ode_period is available in a MATLAB version and an Octave version and a Python version.

Related Data and codes:

predator_prey_ode_period_test

pendulum_ode_period, a MATLAB code which sets up and solves a system of ordinary differential equations (ODE) that represent the behavior of a linear pendulum of length L under a gravitational force of strength G, in order to estimate the period of oscillation.

predator_prey_ode, a MATLAB code which sets up and solves a pair of predator prey ordinary differential equations (ODE).

vanderpol_ode_period, a MATLAB code which sets up and solves the ordinary differential equations (ODE) defining the van der Pol oscillator in order to estimate the period of the limit cycle.

Reference:

1. John D Cook,
   Predator-Prey Period,
   https://www.johndcook.com/blog/2021/07/14/predator-prey-period/
   Posted 14 July 2021
2. Shagi-Di Shih,
   The period of a Lotka-Volterra System,
   Taiwanese Journal of Mathematics,
   Volume 1, Number 4, December 1997, pages 451-470.
3. Joerg Waldvogel,
   The Period in the Volterra-Lotka Predator-Prey Model,
   SIAM Journal on Numerical Analysis,
   Volume 20, Number 6, pages 1264-1272, December 1983.

Source Code:

• lambert_w.m, evaluates the Lambert W function.
• predator_prey_conserved.m, evaluates a conserved quantity.
• predator_prey_deriv.m, defines the right hand side of the ODE.
• predator_prey_equilibrium.m, returns the equilibrium solution of the ODE.
• predator_prey_parameters.m, returns the parameter values of the ODE.
• predator_prey_period_linear.m, returns the period of the limit cycle using only the linear terms.
• predator_prey_period.m, returns the period of the limit cycle.