On a simple single-transistor-based chaotic snap circuit: A maximized attractor dimension at minimized damping and a stable equilibrium

Abstract

A simple chaotic snap circuit based on a single transistor is presented with tunable damping. It suggests, at present, the simplest chaotic snap circuit in the sense that it requires only 9 devices, which offer the minimum number of devices for a chaotic snap circuit. It also suggests the first and simplest circuit realization of either a four-dimensional (4D) chaotic system or a 4th-order (snap) chaotic system that demonstrates a maximized attractor dimension (DL) of a parameter set, or of the entire parameter space of the system, at minimized damping. The tendency of an increase in DL until its peak is illustrated by a decrease in damping. It offers the highest attractor dimension in a category of unit-damping snap chaos. As an initial report, a Clapp oscillator is able to exhibit 4D chaos but does not allow snap chaos. The proposed snap circuit embeds two simple mechanisms: (i) a Clapp oscillator as a simple core engine of oscillations avoiding a need for op-amps, and (ii) a single resistor as a remarkably simple realization of adjustable damping for snap chaos. A current-tunable equilibrium exhibits one of the 4 different types, two of which are of an (unstable) spiral saddle equilibrium, whereas the others are of a spiral stable equilibrium. They reveal the first report on either saddle-equilibrium or stable-equilibrium snap chaos based on a single transistor. Multistability and hidden attractors are demonstrated. The simple circuit offers a novel damping-tunable single-transistor-based approach to such rich dynamics of snap flows through various types of self-excited and hidden attractors.