Nonlinear dynamics and passive control of GLYCOLYTIC oscillations

Abstract

This paper addresses the issues of nonlinear dynamics and passive control of the main first stage of glycolytic oscillations. The Routh–Hurwitz criterion, the Whittaker method and the Floquet theory are utilized to analytically determine the stability boundaries of linear and nonlinear oscillations. Routes to chaos are investigated through bifurcation diagram, Lyapunov exponant, times stories and phase portraits. The passive control scheme is considered to get rid of chaotic oscillations. Results of analytical investigations are validated and complemented by numerical simulations.