Turing instabilities in a glycolysis reaction-diffusion system

Abstract

Pattern dynamics in reaction-diffusion modeling glycolysis are investigated. This paper includes linear stability analysis to deduce the threshold condition for Turing pattern formation and weakly nonlinear analysis to describe the time evolution of the pattern amplitude close to the instability threshold. We will assume that the emerging patterns do not have any spatial structure. We derive a criterion to find the region of parameters for which super/sub-critical Turing instability is possible. Furthermore, we focus on the Turing-Hopf (TH) bifurcation and obtain the reduction of the model to the TH normal forms in order to understand and classify the spatiotemporal dynamics of the model for values of parameters close to the degenerate Turing-Hopf bifurcation point. Our theoretical results are confirmed by numerical simulations.

Keywords:

• Turing instability
• patterns
• glycolysis model
• weakly nonlinear analysis
• amplitude equations
• Turing-Hopf bifurcation

2010 Mathematics Subject Classifications:

• 35K57
• 34C23
• 35B36

Disclosure statement

No potential conflict of interest was reported by the author(s).