Nonlinear dynamics and passive control of GLYCOLYTIC oscillations

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. •A modified Rayleigh oscillator is obtained from Selkov’s model using Tikhonov’s theorem.•Linear and nonlinear stability of unstable oscillations of glycolysis is achieved.•The hysteresis and jump amplitude phenomena are controlled.•Passive control of chaotic glycolytic oscillations is achieved.•Numerical simulations were carried out to confirm the analyticals results.