Modeling of complex dynamics in reaction-diffusion-convection model of cross-flow reactor with thermokinetic autocatalysis

2005 ◽  
pp. 1207-1212
Author(s):  
Tereza Trávníčková ◽  
Igor Schreiber ◽  
Milan Kubíček
Keyword(s):  
Flow Reactor ◽  
Complex Dynamics ◽  
Cross Flow ◽  
Reaction Diffusion ◽  
Convection Model ◽  
Diffusion Convection

Local accumulation times of morphogen gradient with tissue growth

2019 ◽  
Vol 33 (25) ◽  
pp. 1950293
Author(s):  
Jinmeng Yang ◽  
Shuqin Liu ◽  
Hongwei Yin
Keyword(s):  
Reaction Diffusion ◽  
Tissue Growth ◽  
Morphogen Gradients ◽  
Analytic Expressions ◽  
Convection Model ◽  
Diffusion Convection ◽  
Morphogen Transport ◽  
Multicellular Organisms ◽  
Dose Dependent ◽  
Local Accumulation

During development of multicellular organisms, morphogen is a kind of signaling molecules produced at a local region and transported into a development field, which acts as dose-dependent regulators of gene expression, directs and controls cellular differentiation. Some experiments showed that during embryo development, dynamical processes of morphogen transport always accompany the tissue growth. However, how tissue growth affects morphogen gradients remains to be explored. To answer this problem, we propose a reaction-diffusion-convection model for morphogen transport. For this model, we mainly investigate local accumulation times (LATs) of morphogen gradients, which are a measure for time of forming the steady state of morphogen gradients. In this paper, we simplify the method of calculating the LATs and use this method to obtain analytic expressions of the LATs for uniform and linear growth, respectively. Besides, for tissue nonuniform growth, we apply an approximation method of the LATs to study them. This paper shows that tissue growth can shorten the LATs of morphogen gradients.

scholarly journals Theorems and Application of Local Activity of CNN with Five State Variables and One Port

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Gang Xiong ◽  
Xisong Dong ◽  
Li Xie ◽  
Thomas Yang
Keyword(s):  
Bifurcation Diagram ◽  
Complex Dynamics ◽  
Nonlinear Dynamical Systems ◽  
Reaction Diffusion ◽  
Cellular Neural Network ◽  
State Variables ◽  
Nonlinear Dynamical ◽  
Local Activity ◽  
Homogeneous Lattice ◽  
Coupled Cells

Coupled nonlinear dynamical systems have been widely studied recently. However, the dynamical properties of these systems are difficult to deal with. The local activity of cellular neural network (CNN) has provided a powerful tool for studying the emergence of complex patterns in a homogeneous lattice, which is composed of coupled cells. In this paper, the analytical criteria for the local activity in reaction-diffusion CNN with five state variables and one port are presented, which consists of four theorems, including a serial of inequalities involving CNN parameters. These theorems can be used for calculating the bifurcation diagram to determine or analyze the emergence of complex dynamic patterns, such as chaos. As a case study, a reaction-diffusion CNN of hepatitis B Virus (HBV) mutation-selection model is analyzed and simulated, the bifurcation diagram is calculated. Using the diagram, numerical simulations of this CNN model provide reasonable explanations of complex mutant phenomena during therapy. Therefore, it is demonstrated that the local activity of CNN provides a practical tool for the complex dynamics study of some coupled nonlinear systems.

scholarly journals Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Bernard Girau ◽  
César Torres-Huitzil ◽  
Nikolaos Vlassopoulos ◽  
José Hugo Barrón-Zambrano
Keyword(s):  
Large Scale ◽  
Complex Dynamics ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Fpga Implementation ◽  
Cellular Slime Mold ◽  
Reaction Diffusion Model ◽  
Cellular Slime ◽  
Computational Resources ◽  
Embedded Implementation

We consider here the feasibility of gathering multiple computational resources by means of decentralized and simple local rules. We study such decentralized gathering by means of a stochastic model inspired from biology: the aggregation of theDictyostelium discoideumcellular slime mold. The environment transmits information according to a reaction-diffusion mechanism and the agents move by following excitation fronts. Despite its simplicity this model exhibits interesting properties of self-organization and robustness to obstacles. We first describe the FPGA implementation of the environment alone, to perform large scale and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.

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