Semi-analytical solutions for the reversible Selkov model with feedback delay

Semi-analytical solutions for the reversible Selkov, or glycolytic oscillations model, are considered. The model is coupled with feedback at the boundary and considered in one-dimensional reaction-diffusion cell. This experimentally feasible scenario is analogous to feedback scenarios in a continuously stirred tank reactor. The Galerkin method is applied, which approximates the spatial structure of both the reactant and autocatalyst concentrations. This approach is used to obtain a lower-order, ordinary differential equation model for the system of governing equations. Steady-state solutions, bifurcation diagrams and the region of parameter space, in which Hopf bifurcations occur, are all found. The effect of feedback strength and delay response on the parameter region in which oscillatory solutions occur, is examined. It is found that varying the strength of the feedback response can stabilize or destabilize the system while increasing the delay response usually destabilizes the reaction-diffusion cell. The semi-analytical model is shown to be highly accurate, in comparison with numerical solutions of the governing equations.