How can we understand the stability and behavior of enzyme reaction systems? This paper presents a detailed qualitative analysis of the Merkin enzyme reaction system, using qualitative theory and Hopf bifurcation theory. The analysis applies qualitative theory and Hopf bifurcation theory, we detailly discuss the Merkin enzyme reaction system. Using MATLAB software, we present three examples to simulate these conclusions in this paper. The sufficient conditions derived. Local stability can be determined. This research contributes to the understanding of complex biochemical systems. The study is valuable for researchers in systems biology and enzyme kinetics. The study can improve the field.
The Journal of Biological Systems focuses on mathematical and computational approaches to biological problems. This paper fits the journal's scope by providing a detailed mathematical analysis of an enzyme reaction system, exploring its stability and dynamic behavior through qualitative theory and Hopf bifurcation, aligning with the journal's emphasis on quantitative methods.