<p>In this work, we provide an analytical proof of the existence of attracting invariant tori supporting quasiperiodic dynamics in a family of three-dimensional dissipative systems modeling self-oscillatory electronic devices. This family was originally proposed by Kuznetsov, Kuznetsov, and Stankevich, who observed numerically such quasiperiodic dynamics and evidences for the existence of invariant tori. Our results establish the existence of normally hyperbolic attracting tori using recent advances in averaging theory. We also show that the dynamics on these tori are always either periodic or quasiperiodic, and that quasiperiodic motion occurs for a set of parameter values with positive Lebesgue measure. These findings not only confirm and extend the prior numerical observations, but also demonstrate that quasiperiodicity arises with positive probability when parameters are randomly chosen. Moreover, our study highlights the effectiveness of averaging theory as a powerful analytical tool for detecting attractors in applied dynamical systems.</p>