Topolectrical & Nonlinear Circuit Phenomena: A Comprehensive Review

Abstract

Topolectrical circuits, inspired by concepts from topological physics, have emerged as a promising platform for exploring robust edge states, nontrivial topological invariants, and their applications in signal processing and wave propagation. Simultaneously, nonlinear circuits, which exploit the inherent nonlinear behavior of electronic components, are crucial for understanding complex phenomena like chaos, bifurcation, and soliton propagation in electrical networks. This review paper aims to provide a detailed discussion of the state-of-the-art developments in topolectrical and nonlinear circuits, highlighting their fundamental principles, experimental realizations, and potential applications. Special emphasis is placed on the interplay between topology and nonlinearity, demonstrating how these effects can be combined to realize robust, tunable, and multifunctional electrical systems. Illustrative examples, tables, and figures are provided to facilitate understanding of complex phenomena.

KEYWORDS: Topolectrical circuits, Nonlinear circuits, Topological edge states, Chaos, Solitons, Bifurcation, Electrical metamaterials, Signal propagation, Robust circuits