Multiple limit cycles in the chemostat with variable yield.

[1]  A. Balakrishnan,et al.  IMPROVEMENT OF CHEMOSTAT PERFORMANCE VIA NONLINEAR OSCILLATIONS, PART 2. EXTENSION TO OTHER SYSTEMS , 1998 .

[2]  N. Panikov,et al.  Microbial Growth Kinetics , 1995 .

[3]  R. Y. K. Yang,et al.  Improvement of chemostat performance via nonlinear oscillations , 1993 .

[4]  Gail S. K. Wolkowicz,et al.  Mathematical models of microbial growth and competition in the chemostat regulated by cell-bound extracellular enzymes , 1992 .

[5]  Gail S. K. Wolkowicz,et al.  Global dynamics of a mathematical model of competition in the chemostat: general response functions and differential death rates , 1992 .

[6]  N. Panikov,et al.  Observation and explanation of the unusual growth kinetics of Arthrobacter globiformis , 1992 .

[7]  J Hofbauer,et al.  Multiple limit cycles for predator-prey models. , 1990, Mathematical biosciences.

[8]  Arnold L. Demain,et al.  Manual of Industrial Microbiology and Biotechnology , 1986 .

[9]  Robert D. Tanner,et al.  Hopf bifurcations for a variable yield continuous fermentation model , 1982 .

[10]  Doraiswami Ramkrishna,et al.  Theoretical investigations of dynamic behavior of isothermal continuous stirred tank biological reactors , 1982 .

[11]  Paul Waltman,et al.  Bifurcation from a limit cycle in a two predator-one prey ecosystem modeled on a chemostat , 1981 .

[12]  B. Hassard,et al.  Theory and applications of Hopf bifurcation , 1981 .

[13]  J. H. Parish Developmental Biology of Prokaryotes , 1980 .

[14]  Robert D. Tanner,et al.  THE EFFECT OF THE SPECIFIC GROWTH RATE AND YIELD EXPRESSIONS ON THE EXISTENCE OF OSCILLATORY BEHAVIOR OF A CONTINUOUS FERMENTATION MODEL , 1980 .

[15]  Richard Levins,et al.  Coexistence in a Variable Environment , 1979, The American Naturalist.

[16]  Sze-Bi Hsu,et al.  Limiting Behavior for Competing Species , 1978 .

[17]  A. Matin,et al.  Physiological basis of the selective advantage of a Spirillum sp. in a carbon-limited environment. , 1978, Journal of General Microbiology.

[18]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[19]  Sze-Bi Hsu,et al.  A Mathematical Theory for Single-Nutrient Competition in Continuous Cultures of Micro-Organisms , 1977 .

[20]  H. Veldkamp,et al.  Ecological Studies with the Chemostat , 1977 .

[21]  G. Sell,et al.  The Hopf Bifurcation and Its Applications , 1976 .

[22]  H. M. Tsuchiya,et al.  Damped oscillations in continuous culture of Lactobacillus plantarum. , 1976, Journal of general microbiology.

[23]  M. Droop SOME THOUGHTS ON NUTRIENT LIMITATION IN ALGAE 1 , 1973 .

[24]  Bruce R. Levin,et al.  Partitioning of Resources and the Outcome of Interspecific Competition: A Model and Some General Considerations , 1973, The American Naturalist.

[25]  J. Caperon Population Growth Response of Isochrysis Galbana to Nitrate Variation at Limiting Concentrations , 1968 .

[26]  M. Woodbine Continuous Fermentation , 1968, Nature.

[27]  F. Wilson The structure of the level surfaces of a Lyapunov function , 1967 .

[28]  吉沢 太郎 Stability theory by Liapunov's second method , 1966 .

[29]  S. Pirt The maintenance energy of bacteria in growing cultures , 1965, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[30]  E O Powell,et al.  Theory of the chemostat. , 1965, Laboratory practice.

[31]  P. Waltman A bifurcation theorem , 1964 .

[32]  Solomon Lefschetz,et al.  Stability by Liapunov's Direct Method With Applications , 1962 .

[33]  G. Tullock,et al.  Competitive Exclusion. , 1960, Science.

[34]  J. L. Massera Contributions to Stability Theory , 1956 .

[35]  D. Herbert,et al.  The continuous culture of bacteria; a theoretical and experimental study. , 1956, Journal of general microbiology.

[36]  A. Novick,et al.  Description of the chemostat. , 1950, Science.

[37]  J. L. Massera On Liapounoff's Conditions of Stability , 1949 .

[38]  J. Monod,et al.  Recherches sur la croissance des cultures bactériennes , 1942 .