ABSTRACT
We study the dynamical regimes that emerge from the strong coupling between two Chua's circuits with parameters mismatch. For the region around the perfect synchronous state we show how to combine parameter diversity and coupling in order to robustly and precisely target a desired regime. This target process allows us to obtain regimes that may lie outside parameter ranges accessible for any isolated circuit. The results are obtained by following a recently developed theoretical technique, the order parameter expansion, and are verified both by numerical simulations and on electronic circuits. The theoretical results indicate that the same predictable change in the collective dynamics can be obtained for large populations of strongly coupled circuits with parameter mismatches.
ABSTRACT
The mechanism of active phase synchronization in a suspension of oscillatory yeast cells has remained a puzzle for almost half a century. The difficulty of the problem stems from the fact that the synchronization phenomenon involves the entire metabolic network of glycolysis and fermentation, and consequently it cannot be addressed at the level of a single enzyme or a single chemical species. In this paper it is shown how this system in a CSTR (continuous flow stirred tank reactor) can be modelled quantitatively as a population of Stuart-Landau oscillators interacting by exchange of metabolites through the extracellular medium, thus reducing the complexity of the problem without sacrificing the biochemical realism. The parameters of the model can be derived by a systematic expansion from any full-scale model of the yeast cell kinetics with a supercritical Hopf bifurcation. Some parameter values can also be obtained directly from analysis of perturbation experiments. In the mean-field limit, equations for the study of populations having a distribution of frequencies are used to simulate the effect of the inherent variations between cells.
