Bifurcation and Entropy Analysis of a Chaotic Spike Oscillator Circuit Based on the S-Switch

• Published in: Entropy (Basel, Switzerland) Vol. 24; no. 11; p. 1693
• Main Authors: Boriskov, Petr, Velichko, Andrei, Shilovsky, Nikolay, Belyaev, Maksim
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-11-2022; MDPI
• Subjects: Analog circuits; Bifurcations; Chaos theory; chaotic oscillator; Current voltage characteristics; Entropy; Feedback; Field effect transistors; LIF neuron; Matching; Mathematical models; Memory; Metal oxide semiconductor field effect transistors; MOSFETs; Operational amplifiers; Oscillations; Oscillators; Pulse position modulation; RC circuits; reservoir computing; Reservoirs; Schmitt triggers; Semiconductor devices; Step voltage; Time series; Transistors
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e24111693

This paper presents a model and experimental study of a chaotic spike oscillator based on a leaky integrate-and-fire (LIF) neuron, which has a switching element with an S-type current-voltage characteristic (S-switch). The oscillator generates spikes of the S-switch in the form of chaotic pulse position modulation driven by the feedback with rate coding instability of LIF neuron. The oscillator model with piecewise function of the S-switch has resistive feedback using a second order filter. The oscillator circuit is built on four operational amplifiers and two field-effect transistors (MOSFETs) that form an S-switch based on a Schmitt trigger, an active RC filter and a matching amplifier. We investigate the bifurcation diagrams of the model and the circuit and calculate the entropy of oscillations. For the analog circuit, the “regular oscillation-chaos” transition is analysed in a series of tests initiated by a step voltage in the matching amplifier. Entropy values are used to estimate the average time for the transition of oscillations to chaos and the degree of signal correlation of the transition mode of different tests. Study results can be applied in various reservoir computing applications, for example, in choosing and configuring the LogNNet network reservoir circuits.