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GeoGebra

2-species competition

Autore:Pablo Rodríguez-Sánchez

Explanation

This model represents the competitive interactions between two species as a two dimensional autonomous ordinary differential equation (shown in the applet). The main ingredientes of this applet are:
  • The populations of each species: coded as x and y.
  • The nullclines: marked in blue (for species x) and red (for species y).
  • The trajectories in the phase space: represented by green lines (two different trajectories are represented here).
The following parameters can be interactively manipulated:
  • The green points are the initial conditions of this trajectories
  • The r coefficients control the speed of the dynamics
  • The competition coefficients are coded in the array K. They have an straightforward geometrical meaning as the intersection points between nullclines. Thus, the values of K can be modified dragging and dropping the highlighted points in the nullclines
The applet calculates automatically the slope field and the solutions, and classifies the equilibrium points as well as the overall behaviour of the system.

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