The paper presents bifurcation behaviour of a single-phase induction motor. Study of bifurcation of a system gives the complete picture of its dynamical behaviour with the change in system’s parameters. The system is mathematically described by a set of differential equations in the state space. Induction motors are very widely used in domestic and commercial applications. Single-phase capacitor-run induction motors are commonly used as prime movers for fans, pumps and compressors. This paper provides a numerical approach to understand the dynamics of an induction motor in the light of bifurcation and chaos. It is seen that the dynamics of a capacitor-run single-phase induction motor cannot be ascertained by the profile of a single state variable. This paper also attempts to discuss the bifurcation behaviour of the system based on the evolution of different state variables. The bifurcation diagrams drawn looking at different state variables are different in terms of periodicity and route to chaos. The knowledge of the dynamics of the system obtained from bifurcation diagrams give useful guidelines to control the operation of the induction motor depending on the need of an application for better performance.