4910.sagews

from sage.calculus.desolvers import desolve_odeint

var('x,y')
f=[x*(1-y),-y*(1-x)]
t=srange(0,20,0.01)
basesol=desolve_odeint(f,[0.1,0.1],t,[x,y])
baseplot = list_plot(zip(basesol[:,0],basesol[:,1])) + point((0.1, 0.1), color="red")
plotList = [baseplot]

@interact
def _(initPrey=(0.1,5), initPredator=(0.1,5), auto_update=False):
    sol=desolve_odeint(f,[initPrey,initPredator],t,[x,y])
    phase_plane = list_plot(zip(sol[:,0],sol[:,1])) + point((initPrey, initPredator), color="red")
    plotList.append(phase_plane)
    #Show results
    layerPlot = plotList[0]
    for i in [1..len(plotList)-1]:
        layerPlot = layerPlot + plotList[i]
    show(layerPlot)