<p>We explore an examination of a modified Goodwin model, a theoretical framework extensively used in economics to explain the cyclic dependence in employment ratio and wage share. Specifically, our focus centers on the controllable Hopf and Bautin bifurcations within the context of this modified model. These bifurcations serve as crucial analytical tools that allow for a deeper understanding of the mechanisms underlying periodic fluctuations, whether temporary or persistent, observed within economic systems. By incorporating the notion of controllability, we aim to shed light on how certain parameters can be manipulated to influence the occurrence and characteristics of these periodic fluctuations. Through our investigation, we aim to offer insights that may inform policy decisions and strategic interventions aimed at mitigating the impacts of economic fluctuations.</p>