• Biotechnology and Bioprocess Engineering:BBE
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• v.10 no.2
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• pp.115-121
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• 2005

Using a general Saccharomyces cerevisiae as a model strain, continuous ethanol fermentation was carried out in a stirred tank bioreactor with a working volume of 1,500 mL. Three different gravity media containing glucose of 120, 200 and 280 g/L, respectively, supplemented with 5 g/L yeast extract and 3 g/L peptone, were fed into the fermentor at different dilution rates. Although complete steady states developed for low gravity medium containing 120 g/L glucose, quasi-steady states and oscillations of the fermented parameters, including residual glucose, ethanol and biomass were observed when high gravity medium containing 200 g/L glucose and very high gravity medium containing 280 g/L glucose were fed at the designated dilution rate of $0.027\;h^{-1}$. The observed quasi-steady states that incorporated these steady states, quasi-steady states and oscillations were proposed as these oscillations were of relatively short periods of time and their averages fluctuated up and down almost symmetrically. The continuous kinetic models that combined both the substrate and product inhibitions were developed and correlated for these observed quasi-steady states.

• The Pure and Applied Mathematics
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• v.17 no.3
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• pp.211-229
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• 2010

Various types of predator-prey systems are studied in terms of the stabilities of their steady-states. Necessary conditions for the existences of non-negative constant steady-states for those systems are obtained. The linearized stabilities of the non-negative constant steady-states for the predator-prey system with monotone response functions are analyzed. The predator-prey system with non-monotone response functions are also investigated for the linearized stabilities of the positive constant steady-states.

• Bulletin of the Korean Chemical Society
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• v.11 no.6
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• pp.557-560
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• 1990

The transition from one stable steady state branch to another stable steady state branch in a simple metabolic system with positive feedback is discussed with the aid of the bimodal Gaussian probability distribution method. Fluctuations lead to transitions from one stable steady state branch to the other, so that the bimodal Gaussian evolves to a new distribution. We also obtain the fractional occupancies in the two stable steady states in terms of a parameter characterizing conditions of the system.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.133-149
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• 2003

Local stability of steady states of an epidemic model is considered. An age structured S-I-R epidemic model with separable inter-cohort force of infection with external force is considered. Stability result for the nontrivial steady states is obtained.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1827-1840
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• 2013

This paper is concerned with the positive steady states of a diffusive Holling type II predator-prey system, in which two predators and one prey are involved. Under homogeneous Neumann boundary conditions, the local and global asymptotic stability of the spatially homogeneous positive steady state are discussed. Moreover, the large diffusion of predator is considered by proving the nonexistence of non-constant positive steady states, which gives some descriptions of the effect of diffusion on the pattern formation.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.461-467
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• 1998

In spite of significant nonlinearities even in the simplest model, some types of steady-state and dynamic behavior common for nonlinear systems have never been associated with distillation columns. In recent years, multiplicity of steady states has been a subject of much research and is now widely accepted. Subsequently, stability of steady states has been explored. Another phenomenon that. although widely observed in chemical reactors, has not been associated with models of distillation columns is the existence of periodic oscillations. In this article we study the steady-state and dynamic behavior of the azeotropic distillation of the ternary homogeneous system methanol-methyl butyrate-toluene. Our simulations reveal nonlinear behavior not reported in earlier studies. Under certain conditions, the open-loop distillation system shows a sustained oscillation associated with branching to periodic solutions. The limit cycles are accompanied by traveling waves inside the column. Significant underdamped oscillations are also observed over a wide range of product rates.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1393-1407
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• 2023

In this study, we propose a dynamic SEIQRV mathematical model and examine it to comprehend the dynamics of COVID-19 pandemic transmission in the Coimbatore district of Tamil Nadu. Positiveness and boundedness, which are the fundamental principles of this model, have been examined and found to be reliable. The reproduction number was calculated in order to predict whether the disease would spread further. Existing arrangements of infection-free, steady states are asymptotically stable both locally and globally when R₀ < 1. The consistent state arrangements that are present in diseases are also locally steady when R₀ < 1 and globally steady when R₀ > 1. Finally, the numerical data confirms our theoretical study.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.643-655
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• 2001

We discuss the existence of positive solutions to a certain nonlinear elliptic system representing a competition interaction with self-diffusion. The method used here is a fixed point index theory in a positive cone. We give a sufficient condition for the existence of positive solutions.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.251-261
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• 2010

This paper deals with a predator-prey model with Holling type III response function and cross-diffusion subject to the homogeneous Neumann boundary condition. We first give a priori estimates (positive upper and lower bounds) of positive steady states. Then the non-existence and existence results of non-constant positive steady states are given as the cross-diffusion coefficient is varied, which means that stationary patterns arise from cross-diffusion.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.371-385
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• 2004

In this paper, we investigate the uniqueness of positive solutions to weak competition models with self-cross diffusion rates under homogeneous Dirichlet boundary conditions. The methods employed are upper-lower solution technique and the variational characterization of eigenvalues.