Modeling oscillatory behavior in a three variable model of continuous fermentation systems subject to product inhibition
2
Issued Date
2024
Copyright Date
1989
Resource Type
Language
eng
File Type
application/pdf
No. of Pages/File Size
vi, 61 leaves : ill.
Access Rights
open access
Rights
ผลงานนี้เป็นลิขสิทธิ์ของมหาวิทยาลัยมหิดล ขอสงวนไว้สำหรับเพื่อการศึกษาเท่านั้น ต้องอ้างอิงแหล่งที่มา ห้ามดัดแปลงเนื้อหา และห้ามนำไปใช้เพื่อการค้า
Rights Holder(s)
Mahidol University
Bibliographic Citation
Thesis (M.Sc. (Applied Mathematics))--Mahidol University, 1989
Suggested Citation
Mahosut Punpocha Modeling oscillatory behavior in a three variable model of continuous fermentation systems subject to product inhibition. Thesis (M.Sc. (Applied Mathematics))--Mahidol University, 1989. Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/101032
Title
Modeling oscillatory behavior in a three variable model of continuous fermentation systems subject to product inhibition
Alternative Title(s)
แบบจำลองสามตัวแปรของระบบหมักต่อเนื่องซึ่งถูกจำกัดโดยผลิตผล
Author(s)
Advisor(s)
Abstract
A 3-variable model of continuous fermentation processes characterized by product inhibition is studied. It is shown that if the cells to substrate yield is constant, the system can not have periodic solutions. If, on the other hand, the yield term is a variable function of substrate concentration, the model will exhibit oscillations in the cells, substrate and product concentrations in the form of Hopf bifurcation in the underlying system of 3 nonlinear, ordinary differential equations which comprises the model. As time progresses all trajectories in the 3 dimensional solution space tend toward a plane and thus the 3 variable system is equivalent to a model involving only 2 variables. With this result, we are able to obtain the stability condition of limit cycles bifurcating from a non-washout steady state of the 3-variable model, and at the same time rule out the possibility of chaotic trajectories through subsequent bifurcations.
Description
Applied Mathematics (Mahidol University 1989)
Degree Name
Master of Science
Degree Level
Master's degree
Degree Department
Faculty of Science
Degree Discipline
Applied Mathematics
Degree Grantor(s)
Mahidol University