The Search For Small Chaotic Circuits |

Written by Harry Fairhead | |||

Saturday, 21 October 2017 | |||

Chaos and complexity seem to go together, but can you make a chaotic circuit with just small number of parts? A supercomputer search suggests that yes you can and chaos is more common than you might expect. Researchers at the Institute of Nuclear Physics, Polish Academy of Sciences (IFJ PAN) in Krakow have been looking into chaos in electronics. In a paper published in the journal What they did was code up all of the possible circuits. The structure of the circuits, made up of commercially available components, was mapped as a sequence of 85 bits. In the maximum configuration, the modeled circuits consisted of a power source, two transistors, a resistor and six capacitors or induction coils, connected in a circuit containing eight nodes. The strings of bits thus prepared were then subjected to random modifications. The simulations were made on the Cray XD1 supercomputer. At this point you might think that a genetic algorithm was in order but instead circuits were found by blind search. Given that there were 2 Of the 2 million 2500 exhibited interesting behaviour. The reason for using a direct search is that past attempts at implementing genetic algorithms on circuits have been less than successful because crossover tended to produce non-functioning circuits. It seems to be difficult to find a representation that works to produce an offspring that has shared characteristics.
Now we come to an interesting problem. The SPICE simulation wasn't really up to the job of simulating chaotic circuits. This you might expect as the numerical accuracy needed to model chaos is very high. In chaotic systems small changes to the inputs result in large changes to the outputs and this means small errors make the simulation fail. However, when the accuracy was increased it seemed to have little effect on the predictions. As a result there was no choice but to actually build 100 of the most interesting circuits. After some fine tuning, the number of interesting circuits was reduced to 49. The smallest chaotic oscillator used only a single transistor, one capacitor, one resistor and two coils.
Some of the oscillators generated voltage spikes that looked like the sort of thing you measure in biological neural networks:
Before this research only a small number of configurations were known to be chaotic. Now it seems that chaos is not uncommon in small configurations.
## More InformationAtypical transistor-based chaotic oscillators: Design, realization, and diversity Ludovico Minati, Mattia Frasca, Paweł Oświȩcimka, Luca Faes and Stanisław Drożdż ## Related ArticlesThe Programmer's Guide to Chaos Introduction To The Genetic Algorithm
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Last Updated ( Saturday, 21 October 2017 ) |