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Scientific Computing (Psychology 9040a)

Fall, 2021

Lotka-Volterra Predator-Prey Dynamical Model


The following are the Lotka-Volterra equations which can be used to model populations of predators and prey over time:

\[\begin{aligned} \dot{x} &= \alpha x - \beta x y\\ \dot{y} &= \delta x y - \gamma y \end{aligned}\]

where:

the components of the model represent:

The assumptions of the model are:

Simulate the behaviour of this system over time. Start with the following values for the initial states, and the constants:

  1. Plot the population size of predators over time. Overlay a plot of the population size of prey over time.
  2. Plot the trajectory of the system in state-space, in other words plot \(x(t)\) on the horizontal axis and \(y(t)\) on the vertical axis.
  3. Increase the \(\alpha\) constant to \(0.2\) and re-run the simulation. What happens?
  4. Set all constants to 0.20 and re-run the simulation. What happens?
  5. Try the following: \((\alpha,\beta,\delta,\gamma) = (0.2,0.2,0.2,0.0)\). What happens and why?