This paper presents a ring synthetic gene network model described by fractional differential equations, studies the conditions of Hopf bifurcation in the model, and discusses the limit cycle oscillation phenomenon due to the existence of bifurcation, which causes the system to become unstable, and then We propose a method to control the bifurcation behavior in the system, so that the system can be stable over a large range. In addition, the dynamic behavior of the fractional-order model is simulated by triggering a genetic oscillator (a single inhibitory gene) composed of a transistor composed of linear and nonlinear electronic components. The circuit simulation results well verify the theoretical analysis conclusion, and the circuit simulation model can well demonstrate the biological characteristics of gene regulatory networks.