Ludovico Minati, an academic researcher into non-linear systems, discusses the potential of analog circuits to be used to enhance performance in such fields as neuromorphic computation, sensor fusion and secure communications.
There is striking dynamical complexity that is readily accessible with networks of even the simplest analog circuits, so long as they are non-linear.
A fundamental characteristic of brains is that their capabilities are mostly not hardwired by design, but reflect self-organization: brain networks possess so-called emergent properties that cannot be easily inferred from their separate constituent elements. The possibility to engineer a similar approach electronically would likely boost the ability of neuromorphic systems to solve classification and control tasks in a highly size- and energy-efficient manner, with practical implications for both embedded and large-scale computing. However, engineering self-organization remains difficult: leaping from neuromorphic computation by design – amply explored over the past decades – to neuromorphic computation by emergence may look like an insurmountable challenge.
Yet the ability to self-organize is far from unique to networks of neurons and may also be exhibited by elementary electronic oscillators. It is easy to build networks of oscillators that synchronize in patterns not trivially related to their connectivity, and that change dynamically depending on specific settings or inputs. Because this phenomenon can be readily observed even with elementary oscillators, it is possible to implement large networks that, at least in principle, may harbour huge computational capabilities. To stimulate work in this direction, my recent research has explored emergent phenomena through building a diverse set of oscillators including single-transistor circuits [references 1 to 3], CMOS inverter-rings , gas discharge tube circuits  and field-programmable analog arrays (FPAAs) .
For example, one can realize a ring network, wherein each of the 30 nodes is a single-transistor chaotic oscillator comprising only 5 discrete components, and is resistively coupled to its neighbours (Fig. 1, Fig. 2). The circuits can be tuned to oscillate chaotically, in other words, to retain deterministic dynamics but operate in such manner than small fluctuations are rapidly amplified in time .
Fig. 1. Elementary single-transistor oscillator, which can be tuned for periodic or chaotic dynamics by varying R1 (Reproduced from ).
Fig. 2. The STRANGE-1 board, implementing a ring of 30 single-transistor oscillators, resistively coupled to their neighbours (Reproduced from ).
As put by Edward Lorenz: "Chaos: When the present determines the future, but the approximate present does not approximately determine the future." The resulting signals are not at all random, but have a very complex geometric structure that is characteristic of each oscillator; this, for example, may appear as spikes of variable amplitude (Fig. 3).
Fig. 3. Example of spiking chaotic waveform: the spike amplitudes do not vary randomly, but follow a complex deterministic pattern (Reproduced from ).
An interesting phenomenon is that if the oscillators are coupled with intermediate strength, they spontaneously form communities of units that preferentially synchronize with one another (Fig. 4).
Fig. 4. Example of spontaneous community formation (cluster synchronization) by oscillators coupled in a ring; the three matrices represent different sets of components, with associated tolerances (Adapted from ).
The phenomenon, known as cluster synchronization, is seemingly arbitrary, but is ultimately driven in a deterministic manner by the effect that tolerances in component values have on the circuit behaviours . Remarkably, there is evidence of similar phenomena in the brain, which may be the ultimate origin of the modular organization that we observe among its areas .