Numerical Simulation of the Brusselator Model with Spatial Spectral Interpolation Coordination Method

2020 ◽  
Vol 09 (05) ◽  
pp. 708-721
Author(s):  
亭亭 班
Keyword(s):  
Numerical Simulation ◽  
Brusselator Model ◽  
Spectral Interpolation

Memory-Induced Bifurcation and Oscillations in the Chemical Brusselator Model

2020 ◽  
Vol 30 (10) ◽  
pp. 2050151
Author(s):  
Qiqi Deng ◽  
Tianshou Zhou
Keyword(s):  
Numerical Simulation ◽  
Sufficient Conditions ◽  
Reaction System ◽  
Rate Equations ◽  
Transition Rates ◽  
Molecular Memory ◽  
Novel Technique ◽  
Brusselator Model ◽  
Stochastic Oscillations ◽  
Reaction Processes

Previous studies assumed that the reaction processes in the chemical Brusselator model are memoryless or Markovian. However, as long as a reactant interacts with its environment, the reaction kinetics cannot be described as a memoryless process. This raises a question: how do we predict the behavior of the chemical Brusselator system with molecular memory characterized by nonexponential waiting-time distributions? Here, a novel technique is developed to address this question. This technique converts a non-Markovian question to a Markovian one by introducing effective transition rates that explicitly decode the memory effect. Based on this conversion, it is analytically shown that molecular memory can induce bifurcations and oscillations. Moreover, a set of sufficient conditions are derived, which can guarantee that the system of the rate equations for the Markovian reaction system generates oscillations via memory index-induced bifurcation. In turn, these conditions can guarantee that the original non-Markovian reaction system generates stochastic oscillations. Numerical simulation verifies the theoretical prediction. The overall analysis indicates that molecular memory is not a negligible factor affecting a chemical system’s behavior.

Water uptake by substituted amylose tablets: experimentation and numerical simulation

2009 ◽  
Vol 00 (00) ◽  
pp. 090904073309027-8
Author(s):  
H.W. Wang ◽  
S. Kyriacos ◽  
L. Cartilier
Keyword(s):  
Numerical Simulation ◽  
Water Uptake
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