Predator-Prey Model

Model Description

This is a simple predator-prey model with type I or II functional response (depending on parameter choices). The model is also known as the Lotka–Volterra equation. Prey grows logistically and is harvested by predators. In the model, predators are specialists (i.e., they eat only one particular prey species for survival and growth), and their predation pattern can be either type I or II functional response. In type I, the predation rate depends only on the prey density ($b=0$), i.e., how abundant the prey is. In type II, the predation rate is also affected by the processing time of consumption ($b!=0$), i.e., it takes time for some predators to digest/process their meal.

Reference

Lotka, A.J., Elements of Physical Biology, Williams and Wilkins, (1925).

Volterra, V., “Variazioni e fluttuazioni del numero d’individui in specie animali conviventi”, Mem. Acad. Lincei Roma, 2, 31-113, (1926).

Default Dynamics

(Please describe default dynamics for this model.)

$\frac{dx}{dt} = r x (1-\frac{x}{k}) - P(x)y$
Rate of change of prey population.
$\frac{dy}{dt} = -dy + P(x)y$
Rate of change of predator population.
$P(x) = \frac{ax}{bx+1}$
Per capita predation rate as a function of prey density. 
#predator prey model

init x=0.5, y=0.5
par r=2,k=5,d=0.673,a=1,b=.2
p(x) = a*x/(b*x + 1)
dx/dt = r*x*(1-x/k) - p(x)*y
dy/dt = -d*y + p(x)*y

@ total=200,xlo=0,yhi0=7,ylo=0,xhi=8,xp=x,yp=y,nmesh=100
done

Bozicevic M,  Arizona State University. 

You can adjust total time of simulation below.
This model has two state variables. You can set their initial values below.
This model has five parameters. You can set their values below.
Enter the axes to be plotted for this model.