DynamicsKit.jl: A Continuation-Based Framework for Bifurcation Analysis and Operational Robustness Assessment of Chaotic Circuits

Chaotic electronic oscillators generate broadband, noise-like signals for applications such as chaos-based communications. Their practical use requires chaos that persists despite component tolerances and changing conditions. Conventional numerical scans may overlook narrow periodic windows and thus overestimate the robustness of chaos. This paper presents DynamicsKit.jl, an open-source Julia framework integrating numerical continuation, bifurcation analysis, Lyapunov exponents, operating maps, and basin analysis for discrete maps and, through Poincaré return maps, continuous-time systems. Operational robustness is assessed by combining Lyapunov exponent tests, searches for stable periodic orbits, and basin analysis at progressively finer resolutions. The methodology is demonstrated on four representative electronic circuits. For the Vilnius oscillator and a memristive diode-bridge circuit, refined searches reveal periodic windows covering about 13% and 2% of bands that passed an initial low-resolution assessment. Component-tolerance simulations predict periodic behaviour in 29–43% of oscillator realisations at the published set point, 0.3–1.5% at alternative set points with the gain trimmed, and about 3% of memristive-circuit realisations with a lossless inductor. The framework also identifies an unphysical always-on fixed point in a buck-converter map and detects no stable periodic window in the examined boost-converter band. The results assess operational robustness systematically under realistic parameter variations, without claiming mathematical proof.