Cycles and Global Attractors of Reaction Systems

2014 ◽  
pp. 114-125 ◽  
Author(s):  
Enrico Formenti ◽  
Luca Manzoni ◽  
Antonio E. Porreca
Keyword(s):  
Global Attractors ◽  
Reaction Systems

EXISTENCE AND INVARIANCE FOR CONVECTION, DISPERSION, REACTION SYSTEMS WITH PRESSURE

1992 ◽  
Vol 12 (4) ◽  
pp. 443-456 ◽  
Author(s):  
Chunhong Xie ◽  
Taiping He ◽  
Guohong Bai
Keyword(s):  
Reaction Systems

scholarly journals Quasi-stability and continuity of attractors for nonlinear system of wave equations

2021 ◽  
Vol 8 (1) ◽  
pp. 27-45
Author(s):  
M. M. Freitas ◽  
M. J. Dos Santos ◽  
A. J. A. Ramos ◽  
M. S. Vinhote ◽  
M. L. Santos
Keyword(s):  
Wave Equations ◽  
Coupled System ◽  
Global Attractors ◽  
Time Behavior ◽  
Exponential Attractors ◽  
Small Perturbations ◽  
Recent Approach ◽  
Nonlinear Coupled System ◽  
Long Time ◽  
External Forces

Abstract In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces. Using the recent approach by Chueshov and Lasiecka in [21], we prove that this dynamical system is quasi-stable by establishing a quasistability estimate, as consequence, the existence of global and exponential attractors is proved. Finally, we investigate the upper and lower semicontinuity of global attractors under autonomous perturbations.

scholarly journals SiCaSMA: An Alternative Stochastic Description via Concatenation of Markov Processes for a Class of Catalytic Systems

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1074
Author(s):  
Vincent Wagner ◽  
Nicole Erika Radde
Keyword(s):  
Reaction System ◽  
Stochastic Simulation Algorithm ◽  
Test Bed ◽  
Biochemical Reaction Networks ◽  
Full System ◽  
Catalytic Systems ◽  
Reaction Systems ◽  
Sample Paths ◽  
Alternative Description ◽  
Linear Differential

The Chemical Master Equation is a standard approach to model biochemical reaction networks. It consists of a system of linear differential equations, in which each state corresponds to a possible configuration of the reaction system, and the solution describes a time-dependent probability distribution over all configurations. The Stochastic Simulation Algorithm (SSA) is a method to simulate sample paths from this stochastic process. Both approaches are only applicable for small systems, characterized by few reactions and small numbers of molecules. For larger systems, the CME is computationally intractable due to a large number of possible configurations, and the SSA suffers from large reaction propensities. In our study, we focus on catalytic reaction systems, in which substrates are converted by catalytic molecules. We present an alternative description of these systems, called SiCaSMA, in which the full system is subdivided into smaller subsystems with one catalyst molecule each. These single catalyst subsystems can be analyzed individually, and their solutions are concatenated to give the solution of the full system. We show the validity of our approach by applying it to two test-bed reaction systems, a reversible switch of a molecule and methyltransferase-mediated DNA methylation.

Fenton-like reaction system with an analyte-activated catfish effect for enhanced colorimetric and photothermal dopamine bioassay

The Analyst ◽  
2020 ◽  
Author(s):  
Zhengrong Niu ◽  
Hong-Hong Rao ◽  
Xin Xue ◽  
Mingyue Luo ◽  
Xiuhui Liu ◽  
...  
Keyword(s):  
Reactive Oxygen Species ◽  
Advanced Oxidation Processes ◽  
Reaction System ◽  
Reactive Oxygen ◽  
Advanced Oxidation ◽  
Oxygen Species ◽  
Reaction Systems ◽  
Oxidation Processes

Fenton-like reaction systems have been proven to be more efficient as the powerful promoters in advanced oxidation processes (AOPs) due to their resultantly generated reactive oxygen species (ROS) such as...

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