Summary

Personal Anecdote

I remember when chaos entered my life in the '60s (a chaotic decade). I reported to my manager that, as far as I could tell, the circuit behavior of my 20kHz "bang-bang" regulator was controlled by the phases of the moon. He did not take kindly to blaming the moon for my circuit's misbehavior. I changed to a PWM control and the problem went away. Later, when working with a discontinuous mode boost converter similar to that reported by Tse, I saw similar waveforms. In hindsight I feel vindicated in being perplexed. It was 20 years later, in 1984, when the problem was first discussed at a power electronics conference. We now know a lot more about it and more is becoming available.

Solution

The following are some considerations for solving chaos problems.

Stable
Investigators wanting to create chaos often start with nearly unstable circuits. This suggests avoiding chaos by making sure the circuit is robustly stable.

Solvability

Nonlinear
Chaotic circuits are always nonlinear, which means there is no general analytical methods for solving them. There is no a priori criteria for determining if a nonlinear circuit will be chaotic.