Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.
Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.
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DOI：
10.1186/1752-0509-8-45
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发表时间：
2014-04-11
影响因子：
--
通讯作者：
Shiraishi Y
中科院分区：
文献类型：
--
作者：
Wang K;Steyn-Ross ML;Steyn-Ross DA;Wilson MT;Sleigh JW;Shiraishi Y
研究反应扩散系统的非线性模式动力学几乎总是需要系统的一组微分方程的数值解。传统上，这将通过从此类求解器库中选择合适的微分方程求解器来完成，然后编写计算机代码（用C或Matlab等编程语言）来访问所选的求解器并显示作为空间和时间函数的集成结果。这种“基于代码”的方法灵活而强大，但需要一定程度的编程经验。一种现代的替代方法是使用图形编程接口，如Simulink，通过组装和链接从库中绘制的适当代码块来构造数据流图。其结果是状态变量之间相互关系的可视化表示，其输出可以完全等同于基于代码的解决方案。作为教程介绍，我们首先演示了Simulink数据流技术在经典范德波尔非线性振荡器中的应用，并比较了Matlab和Simulink编码方法在求解范德波尔常微分方程中的应用。然后，我们通过数值求解两种不同反应-扩散系统的偏微分方程来展示如何引入空间（一维和二维）：著名的Brusselator化学反应器，以及人类皮层二维连续体模型，其神经元由化学和电（扩散）突触连接。我们比较了Matlab和Simulink实现的相对性能。仿真结果与理论预测结果吻合较好。与传统的编码方法相比，Simulink方框图范式减少了求解反应扩散方程组所需的时间和编程负担。框图的构造不需要高水平的编程技能，图形界面使其本身易于修改和非专家使用。
Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system’s set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This “code-based” approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming skills, and the graphical interface lends itself to easy modification and use by non-experts.
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DOI：
10.1073/pnas.0504136102
发表时间：
2005-07-05
影响因子：
11.1
作者：
Fox, MD;Snyder, AZ;Raichle, ME
通讯作者：
Raichle, ME
DOI：
10.1073/pnas.0308436101
发表时间：
2004-06-22
影响因子：
11.1
作者：
Garfinkel, A;Tintut, Y;Demer, LL
通讯作者：
Demer, LL
影响因子：
2.4
作者：
Chen, PL;Viñals, J
通讯作者：
Viñals, J
DOI：
10.1073/pnas.0601417103
发表时间：
2006-09-12
影响因子：
11.1
作者：
Damoiseaux, J. S.;Rombouts, S. A. R. B.;Beckmann, C. F.
通讯作者：
Beckmann, C. F.
影响因子：
3.8
作者：
Carmon, T;Buljan, H;Segev, M
通讯作者：
Segev, M