Simple electronic circuits that are built of a few components often behave chaotically and in an extremely complicated, nearly unpredictable manner. Physicists from the Institute of Nuclear Physics Polish Academy of Sciences (IFJ PAN) in Cracow have discovered, examined and described dozens of new and unusual circuits of this type. One of these circuits generates voltage pulses very similar to those produced by neurons, only it does it 1000 times faster.
Only a few transistors, resistors, capacitors and induction coils are enough to build electronics circuits that behave in an unpredictable way. Even in simple systems, chaotic oscillations of a complex nature turn out to be not the exception but the norm, according to researchers from the IFJ PAN in Cracow. The team presented 49 new, unusual chaotic electronics oscillators, that were discovered by computer simulations.
"Electronics is usually associated with devices that work precisely and always according to expectations. Our research shows a completely different picture. Even in electronic circuits containing only one or two transistors, chaos is ubiquitous! The predictable and always the same reactions of electronic devices that we all use on an everyday basis do not reflect the nature of electronics but the efforts of designers," said Dr. Ludovico Minati of the IFJ PAN.
Chaos generally means lack of order. In physics, this concept works a little differently. Circuits are said to behave chaotically when very small changes in input parameters result in large changes in output. Since various types of fluctuations are a natural feature of the world, chaotic systems show the wealth of behavior, so great that precise prediction of their reactions is very difficult and often impossible. The circuit can seem to behave randomly, even though its evolution follows a certain complicated pattern.
Chaotic behavior is so complex that there are no methods to effectively design electronic circuits of this type. Physicists from the IFJ PAN approached the problem differently. Instead of building chaotic oscillators from scratch, they decided to discover them. 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 that were prepared were then subjected to random modifications. The simulations were made on the Cray XD1 supercomputer.
"Our search was blind, in a gigantic space offering 2 to a power of 85 possible combinations. During the simulation, we analyzed more or less two million circuits, so an extremely small area of the available space. Of these, about 2,500 circuits exhibited interesting behavior," said Dr. Minati.
He also emphasizes that chaotic electronic oscillators were known about previously. Up to now, it seemed that they occurred in only a few variants and their construction required some effort and an appropriately complex system.
Physicists from IFJ PAN analyzed the behavior of the new circuits using the SPICE program, commonly used in the design of electronic circuits. But in the case of the chaotic behavior, SPICE simulation capabilities turned out to be insufficient. The 100 most interesting circuits were physically built and tested in the laboratory. To improve the quality of the signals generated during the tests, delicate tuning of the component parameters was often performed. Eventually, the number of interesting circuits was reduced to 49. The smallest chaotic oscillator was made of one transistor, one capacitor, one resistor and two induction coils. Most of the circuits were found to be non-trivial, chaotic behavior with a sometimes astonishing scale of complexity. The complexity can be visualized using special graphs. Statistical analyses of the signals generated by the new oscillators did not reveal any traces of two important features found in many self-organizing systems.
"We could talk about multi-fractality if different portions of the voltage variation diagram, magnified in different places in different ways, revealed changes similar to the original characteristics. In turn, we would be dealing with criticality if the circuit was in a state in which it could at any moment switch from regular to the chaotic mode or vice versa. We did not notice these phenomena in the examined oscillators," explained Stanislaw Drozdz, professor at IFJ PAN, Cracow University of Technology. "Critical systems generally have more opportunities for reacting to changes in their own environment. So it is no wonder that criticality is a phenomenon quite often encountered in nature. A lot points to the fact that a system operating in a critical condition is, for example, the human brain."
Of particular interest to the researchers was one of the found oscillators, which generated voltage spikes resembling stimuli typical for neurons. The similarity of impulses was striking here but not complete.
"Our artificial neuron analog proved to be much faster than its biological counterpart: pulses were produced thousands of times more often! If it were not for the lack of criticality and multi-fractality, the speed of operation of this circuit would justify talking about an electronic super-neuron. Perhaps such a circuit exists, only we have not found it yet. At the moment, we have to be satisfied with our 'almost super-neuron'," said Dr. Minati.
The Cracow-based physicists have also demonstrated that as a result of combining the found circuits in pairs, behaviors of even greater complexity appear. Coupled circuits in some situations worked perfectly synchronously. In some, one of the circuits took over the role of leader and in others the mutual interdependence of the oscillators was so complicated that it was revealed only after careful analysis of statistics.
In order to jump-start the development of research about electronic systems that simulate the behavior of the human brain, the diagrams of all circuits found by physicists from the IFJ PAN have been made public. Download them here.
A paper on this research was published in Chaos and can be accessed here.