Time-periodic oscillations in a model for the respiratory process of a bacterial culture

SummaryDeterministic (analytical), stochastic and computer-aided methods have been used to construct the time-periodic (limit cycle) solution of a model suggested by H. Degn to account for the qualitative features of the respiratory process in a Klebsiella Aerogenes bacterial culture.

[1]  K. Shuler,et al.  Stochastic processes in chemical physics , 1969 .

[2]  T. Kurtz.  Limit theorems for sequences of jump Markov processes approximating ordinary differential processes , 1971, Journal of Applied Probability.

[3]  J. Walker,et al.  Book Reviews : THEORY OF BIFURCATIONS OF DYNAMIC SYSTEMS ON A PLANE A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier J. Wiley & Sons, New York , New York (1973) , 1976 .

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

[5]  I. Balslev,et al.  Spatial instability in simple reaction schemes. , 1975, Journal of theoretical biology.

[6]  Manuel G. Velarde,et al.  Convective instability: A physicist's approach , 1977 .

[7]  D. Sattinger.  Topics in stability and bifurcation theory , 1973 .

[8]  D. Sattinger,et al.  Bifurcating time periodic solutions and their stability , 1972 .

[9]  Léon Brenig,et al.  Non-linear Fokker-Planck equation as an asymptotic representation of the master equation , 1977 .

[10]  D. Harrison,et al.  The influence of dissolved oxygen concentration on the respiration and glucose metabolism of Klebsiella aerogenes during growth. , 1967, Journal of general microbiology.

[11]  D. Harrison,et al.  Theory of oscillations of respiration rate in continuous culture of Klebsiella aerogenes. , 1969, Journal of theoretical biology.

[12]  Grégoire Nicolis,et al.  Bifurcation analysis of reaction-diffusion equations—III. Chemical oscillations , 1976 .

[13]  D. E. F. Harrison,et al.  Transient and oscillatory states of continuous culture , 1974 .