Chaos in Analog Electronic Circuits: Comprehensive Review, Solved Problems, Open Topics and Small Example

Abstract

This paper strives to achieve a comprehensive review of chaos in analog circuits and lumped electronic networks. Readers will be guided from the beginning of the investigations of simple electronic circuits to the current trends in the research into chaos. The author tries to provide the key references related to this issue, including papers describing modern numerical algorithms capable of localizing chaotic and hyperchaotic motion in complex mathematical models, interesting full on-chip implementations of chaotic systems, possible practical applications of entropic signals, fractional-order chaotic systems and chaotic oscillators with mem-elements.

The Reinartz Oscillator: Analysis Beyond Regular Behavior of the Circuit

“…Poincare sections reduce 3D problem into 2D map; slices are provided for zero voltage across capacitor and zero current through inductor in series. The geometric shape of observed typical strange attractor resembles popular double-scroll attractor; spirals are evolved around unstable fixed points placed in exterior positions (11). Before merged together, two single-scroll attractors exist and can be captured also via careful experimental measurement.…”

“…To date, chaotic behavior in different forms has been observed in many well-known structures of analog building blocks, starting with continuous-time frequency filters that contain various active elements and ending with digital systems with logic gates. A brief list of these discoveries is summarized in [11] and categorized regarding to the original determination of the circuit. Of course, other comprehensive review papers and books can be found as well.…”

Hybrid Analog Computer for Modeling Nonlinear Dynamical Systems: The Complete Cookbook

“…Moreover, the provided list of papers dealing with the synthesis of chaotic oscillators is by no means complete. For a further study of the design principles leading to chaos generators, we suggest referring to the comprehensive review work [ 46 ]. In addition to the numerous papers cited therein, a vast number of valuable papers can also be found through an internet search.…”

The Intricacies of Sprott-B System with Fractional-Order Derivatives: Dynamical Analysis, Synchronization, and Circuit Implementation

“…In practical applications, electronic circuits of chaotic systems are required [33,34]. Chaotic circuits simplify the investigation and comprehension of chaotic behaviors by offering a physical representation of nonlinear dynamical systems [26,35,36].…”