Dynamical analysis of a biochemical reactor distributed parameter model with time delay

This paper studies a tubular biochemical reactor model with time delay. The dynamics are described by partial functional differential equations. We prove the well-posedness of this system and existence of multiple equilibria. Next, we show the existence of periodic solutions bifurcating from trivial equilibrium profile.

[1]  John Caperon,et al.  Time Lag in Population Growth Response of Isochrysis Galbana to a Variable Nitrate Environment , 1969 .

[2]  Huaxing Xia,et al.  Transient oscillations induced by delayed growth response in the chemostat , 2005, Journal of mathematical biology.

[3]  A. Bush,et al.  The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater. , 1976, Journal of theoretical biology.

[4]  Robert H. Martin,et al.  Nonlinear operators and differential equations in Banach spaces , 1976 .

[5]  T. Thingstad,et al.  Dynamics of chemostat culture:the effect of a delay in cell response. , 1974, Journal of theoretical biology.

[6]  M. R. Droop,et al.  Vitamin B12 and Marine Ecology. IV. The Kinetics of Uptake, Growth and Inhibition in Monochrysis Lutheri , 1968, Journal of the Marine Biological Association of the United Kingdom.

[7]  C. C. Travis,et al.  Existence, stability, and compactness in the -norm for partial functional differential equations , 1978 .

[8]  Gail S. K. Wolkowicz,et al.  Bifurcation Analysis of a Chemostat Model with a Distributed Delay , 1996 .

[9]  R. E. Wilson,et al.  Fermentation Process Control, Population Dynamics of a Continuous Propagator for Microorganisms , 1954 .

[10]  Jérôme Harmand,et al.  A SEMILINEAR PARABOLIC BOUNDARY-VALUE PROBLEM IN BIOREACTORS THEORY , 2004 .

[11]  Jianhong Wu Theory and Applications of Partial Functional Differential Equations , 1996 .

[12]  R. Martin,et al.  Reaction-diffusion systems with time delays: monotonicity, invariance, comparison and convergence. , 1991 .

[13]  Hal L. Smith,et al.  Abstract functional-differential equations and reaction-diffusion systems , 1990 .

[14]  Gail S. K. Wolkowicz,et al.  Global Asymptotic Behavior of a Chemostat Model with Discrete Delays , 1997, SIAM J. Appl. Math..

[15]  Tao Zhao Global Periodic-Solutions for a Differential Delay System Modeling a Microbial Population in the Chemostat , 1995 .

[16]  Ioannis G. Stratis,et al.  PERIODIC SOLUTIONS TO RETARDED AND PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS , 2022 .

[17]  Jan Prüss,et al.  Periodic solutions of semilinear evolution equations , 1979 .

[18]  Denis Dochain,et al.  Modelling of continuous microbial cultivation taking into account the memory effects , 2000 .

[19]  Denis Dochain,et al.  Asymptotic Behavior and Stability for Solutions of a Biochemical Reactor Distributed Parameter Model , 2008, IEEE Transactions on Automatic Control.

[20]  N. Macdonald,et al.  Time delay in simple chemostat models , 1976, Biotechnology and bioengineering.

[21]  Khalil Ezzinbi,et al.  PERIODIC SOLUTIONS FOR SOME PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS , 2006 .

[22]  乔花玲,et al.  关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解 , 2003 .