Multiplicity and stability analysis of continuous pre-fermentation of cheese culture |
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| Institution: | 1. Bioprocess Research Division, Korea Research Institute of Bioscience and Biotechnology, Yusong, Taejon 305-600, South Korea;2. Department of Chemical and Biochemical Engineering, University of California, Irvine, CA 92697, USA;1. Department of Drug Metabolism, State Key Laboratory of Bioactive Substance and Function of Natural Medicines, Beijing Laboratory of Non-Clinical Drug Metabolism and PK/PD Study, Beijing Key Laboratory of Active Substance Discovery and Druggability Evaluation, Institute of Materia Medica, Peking Union Medical College and Chinese Academy of Medical Sciences, 1 Xian Nong Tan Street, Beijing 100050, PR China;2. State Key Laboratory of Bioactive Substance and Function of Natural Medicines, Beijing Key Laboratory of Active Substance Discovery and Druggability Evaluation, Institute of Materia Medica, Peking Union Medical College and Chinese Academy of Medical Sciences, 1 Xian Nong Tan Street, Beijing 100050, PR China;3. Chinese Academy of Medical Sciences Key Laboratory of Anti-DR TB Innovative Drug Research, Institute of Materia Medica, Peking Union Medical College and Chinese Academy of Medical Sciences, 1 Xian Nong Tan Street, Beijing 100050, PR China;1. Lasers Department, National Institute for Lasers, Plasma and Radiation Physics, Magurele, Bucharest, Romania;2. University of Craiova, Faculty of Mathematics and Natural Sciences, 200585 Craiova, Romania;3. University of Bucharest, Department of Biochemistry and Molecular Biology, Bucharest, Romania;4. Faculty of Physics, University of Bucharest, Magurele, Bucharest, Romania;5. University of Medicine and Pharmacy Carol Davila, Bucharest, Romania |
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| Abstract: | Unlike the usual multiplicity of steady states in continuous stirred-tank bioreactors caused by the non-monotonicity of substrate dependent rate expression(s), this paper described a different multiplicity caused by the effect of H+]. The multiplicity of the bioreactor for cheese pre-fermentation is also described in this paper. Phase plane analysis shows clearly the separatrix that separates the zone of stable steady state from that of unstable steady state. The steady state becomes unique and elimination of multiplicity by supplying a seed stream, which also guarantees stability. Stability analysis of the multiple steady state shows that unlike the usual necessary condition (∂μ/∂S>0), this process stability demands the opposite necessary condition (∂μ/∂H+]<0). |
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