Diversity of temporal self-organized behaviors in a biochemical system.

The numerical study of a glycolytic model formed by a system of three delay-differential equations revealed a notable richness of temporal structures which included the three main routes to chaos, as well as a multiplicity of stable coexisting states. The Feigenbaum, intermitency and quasiperiodicity routes to chaos can emerge in the biochemical oscillator. Moreover, different types of birhythmicity, trirhythmicity and hard excitation emerge in the phase space. For a single range of the control parameter it can be observed the coexistence of two quasiperiodicity routes to chaos, the coexistence of a stable steady state with a stable torus, and the coexistence of a strange attractor with different stable regimes such as chaos with different periodic regimes, chaos with bursting behavior, and chaos with torus. In most of the numerical studies, the biochemical oscillator has been considered under periodic input flux being the mean input flux rate 6 mM/h. On the other hand, several investigators have observed quasiperiodic time patterns and chaotic oscillations by monitoring the fluorescence of NADH in glycolyzing yeast under sinusoidal glucose input flux. Our numerical results match well with these experimental studies.