Application of the Lyapunov exponent to detect noise-induced chaos in oscillating microbial cultures

Oscillating microbial processes can, under certain conditions, gravitate into chaotic behavior induced by external noise. Detection and control of chaos are important for the survival of the microorganisms and to operate a process usefully. In this study the largest Lyapunov exponent is recommended as a convenient and reliable index of chaos in continuous oscillating cultures. For the growth of Saccharomyces cerevisiae as a model system, the exponents increase with the oxygen mass transfer coefficient and decrease as the dilution rate increases. By comparing with the corresponding time-domain oscillations determined earlier, it is inferred that weakly oscillating cultures are less likely to be driven to chaotic behavior. The main carbon source, glucose, is quite robust to chaotic destabilization, thus enhancing its suitability as a manipulated variable for bioreactor control.