3. Interactive Applications (Java applets)

In the sections below some Java applets can be used to investigate the behavior of some dynamical systems. The exercises can be solved both theoretically and graphically with the applets.

3.1. Examples

• Roundoff
• Function-plot
• Logistic-map
• 1-dimensional orbits
• 2-dimensional orbits
• Hénon attractor

3.2. Exercises

i. Investigate the forward orbit of the baker map, use the roundoff applet, with different startpoints in [0,1]. What happens ?

ii. Investigate the behavior of the logistic map, use the logistic_map-applet. What happens for different values of m in ]0,4] ?

iii. Describe the forward orbits of cos(x) and . You may use the orbits applet.

iv. Investigate the two-dimensional system: X _t+1= aX _t + bX _t-1. What happens for different values of a and b ? You may use the two_dim applet.