We study synchronization due to noise and/or coupling in dynamical systems with multiple time scales. The challenge of taming nonuniformly hyperbolic structures is faced with non-standard geometric singular perturbation theory. An application focus is on biochemical oscillation reactions, with potential scope for wave fronts under noise.
pH-dependent reaction kinetics
The 4-variable model under consideration includes substrate transformation, product outflow, and exchange with the environment. Reaction rates are strongly influenced by pH-values.
Figure 1: Urea−urease reaction confined to lipid vesicles
Figure 2. Phase portraits for two model reduction schemes. Although the nullclines are identical, flow field and limit cycles are qualitatively different.
