Atypical transistor-based chaotic oscillators: Design, realization, and diversity

Abstract

In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date. These circuits are atypical as they do not trivially map onto known topologies or variations thereof. They feature diverse spectra and predominantly anti-persistent monofractal dynamics. Notably, we recurrently found a circuit comprising one resistor, one transistor, two inductors, and one capacitor, which generates a range of attractors depending on the parameter values. We also found a circuit yielding an irregular quantized spike-train resembling some aspects of neural discharge and another one generating a double-scroll attractor, which represent the smallest known transistor-based embodiments of these behaviors. Through three representative examples, we additionally show that diffusive coupling of heterogeneous oscillators of this kind may give rise to complex entrainment, such as lag synchronization with directed information transfer and generalized synchronization. The replicability and reproducibility of the experimental findings are good.

High-dimensional dynamics in a single-transistor oscillator containing Feynman-Sierpiński resonators: Effect of fractal depth and irregularity

“…The circuit size is therefore relatively low compared to the known designs of hyperchaotic oscillators: in particular, it appears noteworthy that complex components such as multipliers are absent and the only active, non-linear component in the present circuit is a transistor. Insofar as some meaningful analogy can be postulated between the behavior of non-linear electronic circuits and that of neurons 24,37 , two remarks of potential neuroscientific relevance can be made. First, the depth of truncated fractals plausibly impacts dynamical complexity in a general sense.…”

“…The chosen circuit was introduced in Ref. 24, wherein a large-scale random search recurrently identified it as the smallest topology giving rise to chaotic behavior. It is an autonomous oscillator powered by a fixed voltage source V s connected via a resistor whose value R is treated as control parameter, as a function of which diverse dynamics including spiral, phase-coherent attractors, attractors resembling the Rössler funnel attractor and spiking attractors can be observed.…”

“…Similarly to Ref. 24, a ceramic substrate was chosen for circuit realization, and the NPN bipolar junction transistor was of type PRF949 (NXP Semiconductor, Eindhoven, The Netherlands). Voltage v C1 was selected as the physical variable of interest and, to minimize loading effects, a low-capacitance preamplifier of type MAX4200 (Maxim Inc., San Jose CA, USA) was provisioned.…”

“…As in Ref. 24, the resistor R was implemented as a trimmer, and manually adjusted to explore different regions of chaotic operation for each circuit. The resulting circuit board was equipped with six U.FL coaxial sockets, allowing connection to the external power sup-ply for the oscillator (V CC = +2.5 V) and the preamplifier (V DD = +5 V, V EE = −1 V), and connection to an oscilloscope for time-series digitization or to a network analyzer for frequency response measurement.…”

“…having D > 3. We do so in the context of an elementary, autonomous single-transistor oscillator, which is the smallest member of a large family of atypical chaotic circuits that were recently obtained by means of a heuristically-driven random search procedure 24 . We focus on a specific fractal structure, i.e., the Feynman-Sierpiński ladder or resonator, which has been introduced in Ref.…”