Simplest transistor-based chaotic circuit with extreme events: Statistical characterization, synchronization, and analogy with interictal spikes

Abstract

This paper investigates the simplest autonomous chaotic circuit capable of generating extreme events, comprising a DC voltage source, a series resistor, a capacitor, three inductors, and two bipolar transistors. The statistical properties and synchronization of the extreme events generated by the system are characterized using a simplified equation model, realistic SPICE simulations, and experimental circuit measurements. Heavy-tailed amplitude distributions and Poisson-like inter-event intervals are uncovered, confirming the existence and uncorrelated nature of the extreme events generated in this elementary circuit. Furthermore, a regime is identified where the extreme events synchronize significantly more strongly than the underlying lower-amplitude continuous activity that paces the dynamics, and a novel approach to visualize this situation is introduced. By drawing a tentative parallel with the interictal spikes observed in the neuroelectrical recordings of epilepsy patients, the study proposes that the analog chaotic circuit under consideration could, in the future, serve as a physical model for studying epileptic-like dynamics in electronic networks.