Circuitry inspired by prime numbers creates chaotic signals : Page 2 of 3

May 23, 2019 //By Jean-Pierre Joosting
Circuitry inspired by prime numbers creates chaotic signals
A small, efficient device that generates "chaotic signals" and is suitable for emerging applications such as realizing wireless networks of sensors has been developed by researchers at Tokyo Institute of Technology.

The research team started from the idea that cycles that have periods set by different prime numbers cannot develop a fixed phase relationship. Surprisingly, this principle seems to have emerged in the evolution of several species of cicadas, whose life cycles follow prime numbers of years, to avoid synchronizing with each other and with predators. For example, if one tries to "tie together" oscillators with periods set to the first three prime numbers (3, 5 and 7), the resulting signals are very complicated and chaos can readily be generated (Figure 1).


The simple idea underlying the design of the circuit is linking together some ring oscillators having lengths equal to the smallest odd prime numbers, such as 3, 5 and 7 (top). Even a simple sum between sine waves having such periods yields a complicated-looking signal (bottom), but the interactions between real oscillators lead to a much richer scenario. Image courtesy of Ludovico Minati.

The design started from the most traditional oscillator found in integrated circuits, called the "ring oscillator," which is small and does not require reactive components (capacitors and inductors). Such a circuit was modified so that the strengths of ring oscillators having three, five and seven stages could be controlled independently, along with the tightness of their linkages. The device could generate chaotic signals over a wide frequency spectrum, from audible frequencies to the radio band (1 kHz to 10 MHz).

"Moreover, it could do so at a rather low power consumption, below one-millionth of a watt," explains Dr. Hiroyuki Ito, head of the laboratory where the prototype was designed.


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