Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK

BMC Systems Biology

Yoichi Shiraishi³  Jamie W Sleigh¹  Marcus T Wilson²  D Alistair Steyn-Ross²  Moira L Steyn-Ross²  Kaier Wang² 

[1] Waikato Clinical School, The University of Auckland, Waikato Hospital, Hamilton 3204, New Zealand;School of Engineering, The University of Waikato, Private Bag 3105, Hamilton 3240, New Zealand;Department of Product Science and Technology, Gunma University, 29-1 Hon-cho, Ohta-shi, Gunma 373-0052, Japan

关键词: Turing–Hopf pattern;    Cortical model;    Brusselator model;    SIMULINK modelling;   

Others  :  866494
DOI  :  10.1186/1752-0509-8-45

 received in 2014-02-19, accepted in 2014-04-07,  发布年份 2014

【 摘 要 】

Background

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.

Results

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.

Conclusions

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.

【 授权许可】

   
2014 Wang et al.; licensee BioMed Central Ltd.

【 图 表 】

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