Logistisches Wachstum

Im so genannten Verhulst-Modell werden das lineare und das beschränkte Wachstum berücksichtigt. Dies spiegelt sich in der (vereinfachten) Formel

x(t+1)=r.x(t).[1 - x(t)]

Beispiel:

Code:

import java.awt.*;
import java.awt.event.*;

/**
 *
 * @author  nus
 */
public class LogwachsAppl extends java.applet.Applet implements ActionListener {
    
    public TextField eingabe;
    public Button ok;
    
    /** Initialization method that will be called after the applet is loaded
     *  into the browser.
     */
    public void init() {
        setBackground(Color.white);
        setLayout(new FlowLayout());
        Label was = new Label("a: ");
        add(was);
        eingabe = new TextField("2.5",6);
        add(eingabe);
        ok = new Button("ok");
        add(ok);
        ok.addActionListener(this);
    }
    
    public void actionPerformed(ActionEvent e) {
        if (e.getSource() == ok) repaint();
    }    
    
    public double verhulst(double x, double a) {
     return a*x*(1-x);   
    }
    
    public void paint(Graphics bs) {        
        double ys=0.01;
        double yz=0.01;
        double a = Double.parseDouble(eingabe.getText());
        for (double x=0.01;x<3.5;x+=0.01) {
            ys = verhulst(ys,a);
            bs.setColor(Color.blue);
            bs.fillRect((int)(x*100+25),400-(int)(ys*400),2,2);
            bs.setColor(Color.red);
            bs.drawLine((int)(x*100+24), 400 - (int)(yz*400),(int)(x*100+25),400 - (int)(ys*400));
            yz=ys;
        }
    }
}