scholarly journals Dynamical behaviors of the stochastic multimolecule oscillatory reaction model with Poisson jumps

2020 ◽  
Author(s):  
Yongchang Wei ◽  
Zongbin Yin
Keyword(s):  
Reaction Model ◽  
Oscillatory Reaction ◽  
Poisson Jumps ◽  
Dynamical Behaviors

scholarly journals Long-time dynamics of a stochastic multimolecule oscillatory reaction model with Poisson jumps

2021 ◽  
Vol 7 (2) ◽  
pp. 2956-2972
Author(s):  
Yongchang Wei ◽  
◽  
Zongbin Yin ◽  
Keyword(s):  
Existence And Uniqueness ◽  
Reaction Model ◽  
Oscillatory Reaction ◽  
Poisson Jumps ◽  
Time Dynamics ◽  
Dynamical Behaviors ◽  
Random Attractors ◽  
Long Time ◽  
Global Positive Solution ◽  
Lyapunov Technique

<abstract><p>This paper reveals dynamical behaviors in the stochastic multimolecule oscillatory reaction model with Poisson jumps. First, this system is proved to have a unique global positive solution via the Lyapunov technique. Second, the existence and uniqueness of general random attractors for its stochastic homeomorphism flow is proved by the comparison theorem, and meanwhile, a criterion for the existence of singleton sets is obtained. Finally, numerical simulations are used to illustrate the predicted random attractors.</p></abstract>

Complex bifurcations in the oscillatory reaction model

2016 ◽  
Vol 87 ◽  
pp. 84-91 ◽  
Author(s):  
Branislav Stanković ◽  
Željko Čupić ◽  
Stevan Maćešić ◽  
Nataša Pejić ◽  
Ljiljana Kolar-Anić
Keyword(s):  
Reaction Model ◽  
Oscillatory Reaction

Intensification of cooling in a batch reactor with an exothermic reaction by nonisothermal control in stable pseudostationary states

1984 ◽  
Vol 49 (11) ◽  
pp. 2566-2578 ◽  
Author(s):  
Josef Horák ◽  
Petr Beránek ◽  
Dagmar Maršálková
Keyword(s):  
Batch Reactor ◽  
Exothermic Reaction ◽  
Reaction Model ◽  
Order Reaction ◽  
Zero Order ◽  
Coolant Temperature ◽  
Inlet Temperature ◽  
Adaptive Parameter ◽  
Zero Order Reaction ◽  
Set Up

An algorithm is set up and tested for the temperature control of a batch reactor consisting in jump changes in the inlet temperature of entering coolant. This temperature is so chosen that its difference from the temperature of the reaction mixture is near the highest difference at which the stable pseudostationary state of the system still exists. For the prediction of the new coolant inlet temperature, a zero-order reaction model is used with an adaptive parameter estimated from the experimentally established value of the maximum of the reaction mixture overheating at the previous coolant temperature.

scholarly journals Complex Dynamical Behaviors of a Mixed Duopoly Game Based on Intellectual Property Rights Protection

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Tong Chu ◽  
Yu Yu ◽  
Xiaoxue Wang
Keyword(s):  
Intellectual Property ◽  
Property Rights ◽  
Intellectual Property Rights ◽  
Mixed Duopoly ◽  
Fractal Structures ◽  
Rights Protection ◽  
Intellectual Property Rights Protection ◽  
Dynamical Behaviors ◽  
Property Rights Protection ◽  
Coexistence Of Attractors

Based on the oligopoly game theory and the intellectual property rights protection policy, we investigate the complex dynamical behaviors of a mixed duopoly game with quadratic cost. In the new system, a few parameters are improved by considering intellectual property rights protection and the stability conditions of the Nash equilibrium point are discussed in detail. A set of the two-dimensional bifurcation diagrams is demonstrated by using numerical modeling, and these diagrams show abundant complex dynamical behaviors, such as coexistence of attractors, different bifurcation, and fractal structures. These dynamical properties can present the long-run effects of strengthening intellectual property protection.

Numerical Approximations to Solution of Biochemical Reaction Model

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Ahmet Gökdogan ◽  
Mehmet Merdan
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Transformation Method ◽  
Reaction Model ◽  
Biochemical Reaction ◽  
Graphical Form ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.

Gas Cell Infrared and Attenuated Total Reflection Infrared Spectroscopic Studies for Organic–Inorganic Interactions in Adsorption of Fulvic Acid on the Goethite Surface Generating Carbon Dioxide

2021 ◽  
pp. 000370282199121
Author(s):  
Yuki Nakaya ◽  
Satoru Nakashima ◽  
Takahiro Otsuka
Keyword(s):  
Carbon Dioxide ◽  
Activation Energy ◽  
Fulvic Acid ◽  
Spectroscopic Studies ◽  
Reaction Model ◽  
Total Reflection ◽  
Attenuated Total Reflection ◽  
Gas Cell ◽  
Rate Determining Step ◽  
Ir Spectroscopic

The generation of carbon dioxide (CO2) from Nordic fulvic acid (FA) solution in the presence of goethite (α-FeOOH) was observed in FA–goethite interaction experiments at 25–80 ℃. CO2 generation processes observed by gas cell infrared (IR) spectroscopy indicated two steps: the zeroth order slower CO2 generation from FA solution commonly occurring in the heating experiments of the FA in the presence and absence of goethite (activation energy: 16–19 kJ mol–1), and the first order faster CO2 generation from FA solution with goethite (activation energy: 14 kJ mol–1). This CO2 generation from FA is possibly related to redox reactions between FA and goethite. In situ attenuated total reflection infrared (ATR-IR) spectroscopic measurements indicated rapid increases with time in IR bands due to COOH and COO– of FA on the goethite surface. These are considered to be due to adsorption of FA on the goethite surface possibly driven by electrostatic attraction between the positively charged goethite surface and negatively charged deprotonated carboxylates (COO–) in FA. Changes in concentration of the FA adsorbed on the goethite surface were well reproduced by the second order reaction model giving an activation energy around 13 kJ mol–1. This process was faster than the CO2 generation and was not its rate-determining step. The CO2 generation from FA solution with goethite is faster than the experimental thermal decoloration of stable structures of Nordic FA in our previous report possibly due to partial degradations of redox-sensitive labile structures in FA.

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