Applying Singular Perturbation Theory for Reducing the Size of Dynamic Model of the Electronic Circuits

Abstract

The dynamic modelling of nonlinear electronic circuits often results in high-dimensional systems of differential equations that are computationally expensive to solve, particularly when incorporating parasitic elements with widely varying time scales. This research proposes a dimensionality reduction framework utilizing singular perturbation theory applied to the chaotic Chua circuit. By decomposing the system dynamics into "slow" (outer) and "fast" (inner) time scales, and invoking Tikhonov’s theorem to validate the asymptotic correctness, a reduced-order model is derived. A uniform approximation is subsequently constructed by mathematically matching the boundary layer transients with the steady-state behaviour. Numerical simulations compare this approximation against the full system solved via standard ODE solvers, revealing that the uniform approximation achieves high fidelity with negligible absolute errors. The results confirm that singular perturbation is an effective technique for minimizing computational cost without compromising dynamical accuracy, presenting significant potential for scaling to higher-dimensional problems.