Branching analysis of T-periodic solutions in nonlinear biochemical systems using reductive perturbation method

Abstract

The application of reductive perturbation method (RPM) towards a detailed analysis of the occurences and bifurcations of various oscillatory patterns in general multi-equation system is discussed. RPM was used to construct a complete bifurcation diagram without resorting to any extensive numerical tracing or analysis. Optimization was used to give the connections between various branches in the parameter space subject to the constraints determined by bifurcation theory. It was found that by applying the Floquet theory and multiple time scales, RPM gives the perturbation equations that enable the determination of the parameter conditions and help in the analysis of bifurcation of T-periodic solutions.