English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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 <inline-formula> <tex-math notation="LaTeX">$(D_{\mathrm {L}})$ </tex-math></inline-formula> of a parameter set, or of the entire parameter space of the system, at minimized damping. The tendency of an increase in <inline-formula> <tex-math notation="LaTeX">$D_{\mathrm {L}}$ </tex-math></inline-formula> 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: (<inline-formula> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula>) a Clapp oscillator as a simple core engine of oscillations avoiding a need for op-amps, and (<italic>ii</italic>) 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.

On a Simple Single-Transistor-Based Chaotic Snap Circuit: A Maximized Attractor Dimension at Minimized Damping and a Stable Equilibrium