Two gene oscillator: -
Consider the feedback system composed of two genes expressing proteins A (activator) and R (repressor), in which we denote by A, R, mA, and mR, the concentrations of the activator protein, the repressor protein, the mRNA for the activator protein, and the mRNA for the repressor protein, respectively. The differential equation model corresponding to this system is given by
Determine parameter conditions under which this system admits a stable limit cycle. Validate your findings through simulation.