Uniqueness of steady states for a certain chemical reaction
نویسندگان
چکیده
In [1], Samoilov, Plyasunov, and Arkin provide an example of a chemical reaction whose full stochastic (Master Equation) model exhibits bistable behavior, but for which the deterministic (mean field) version has a unique steady state. The reaction that they provide consists of an enzymatic futile mechanism driven by a second reaction which induces " deterministic noise " on the concentration of the forward enzyme (through a somewhat artificial activation and deactivation of this enzyme). The model is as follows:
منابع مشابه
The Effect of Coking on Kinetics of HDS Reaction under Steady and Transient States
A study was made of the coking of a commercial fresh sulfide Ni-Mo/Al2O3 catalyst in a fixed-bed reactor. The catalyst was coked using different coke precursors in the gas oil under accelerated conditions at temperatures of 400 to 450°C to yield different deactivated catalysts containing 2-20 wt% C. Two cases were studied; crushed catalyst without diffusional ...
متن کاملNode Balanced Steady States: Unifying and Generalizing Complex and Detailed Balanced Steady States.
We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we introduce a graph, called a reaction graph, that has one edge for each reaction but potentially multiple nodes for each complex. A special class of steady state...
متن کاملChaos Control in a Non-Isothermal Autocatalytic Chemical Reactor
In this paper, a reaction system consisting of two parallel, non-isothermal autocatalytic reactions in a Continuous Stirred Tank Reactor (CSTR) has been considered. Reactor chaotic behavior is possible for certain values of system parameters. Two types of controllers are designed and compared in order to control both the reactor temperature and the product concentration. T...
متن کاملAnalyzing multistationarity in chemical reaction networks using the determinant optimization method
Multistationary chemical reaction networks are of interest to scientists and mathematicians alike. While some criteria for multistationarity exist, obtaining explicit reaction rates and steady states that exhibit multistationarity for a given network—in order to check nondegeneracy or determine stability of the steady states, for instance—is nontrivial. Nonetheless, we accomplish this task for ...
متن کاملGeneralized Mass-Action Systems and Positive Solutions of Polynomial Equations with Real and Symbolic Exponents (Invited Talk)
Dynamical systems arising from chemical reaction networks with mass action kinetics are the subject of chemical reaction network theory (CRNT). In particular, this theory provides statements about uniqueness, existence, and stability of positive steady states for all rate constants and initial conditions. In terms of the corresponding polynomial equations, the results guarantee uniqueness and e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005