Constrained Duffing Map

This chaotic generator is based on the discrete Duffing map. Under certain settings it reproduces the chaotic behavior of the Duffing map. However, as the system can very easily blow up, some constraints have been put in place to prevent the numbers in the system to grow out of control under certain settings. That is where the Limit and Constraint Range (C Rng) knobs come in.

The system is controlled by the values of alpha and beta, which by default are set to alpha = 2.75 and beta = 0.2, which will result in chaotic behavior. But as these values are varied, the system can easily get stuck. You can then vary alpha and beta and hit the inject button to reset the system.

Limit determines at what level the values will be restrained. When this happens, new random value are introduced instead of the old values, bringing the system back to an acceptable range. The C Range knob will determine the range of the random numbers that will be used. But it is not necessary to understand the details. The best thing to do is to simply play with these knobs and use your ears. There are many interesting kinds of chaotic behavior that will arise at different combinations of these parameters.

The Rand button sets the Alpha and Beta knobs to random values for quickly exploring different combinations. But keep in mind that you may also need to inject new values in some cases when the system gets stuck, using the inject button. The small R toggles next to the Limit and C Range knobs determine whether or not those knobs will be randomized.

The respective scale and offset knobs allow you to easily adjust the range of produced values for musical purposes. Keep in mind that if the scale knobs are set to zero there will be no output.

There are 3 outputs: for the X and Y values, and for the difference between the two. These have an additional attenuator to control the output level, which multiply the signal after the scale and offset.

It is usually a good idea to connect the outputs to oscilloscopes, to have a clearer idea about what's going on, especially regarding ranges.

This module is part of the Benard Mega Bundle Vol. 3.