Publication Date:
2014-04-12
Description:
Background: Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requiresnumerical solution of the system's set of defining differential equations. Traditionally, this wouldbe done by selecting an appropriate differential equation solver from a library of such solvers, thenwriting computer codes (in a programming language such as C or MATLAB) to access the selectedsolver and display the integrated results as a function of space and time. This "code-based" approachis flexible and powerful, but requires a certain level of programming sophistication. A modernalternative is to use a graphical programming interface such as SIMULINK to construct a data-flowdiagram by assembling and linking appropriate code blocks drawn from a library. The result is avisual representation of the inter-relationships between the state variables whose output can be madecompletely equivalent to the code-based solution. Results: As a tutorial introduction, we first demonstrate application of the SIMULINK data-flow techniqueto 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 introducespace (in one and two dimensions) by solving numerically the partial differential equations for twodifferent reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuummodel for a two-dimensional sheet of human cortex whose neurons are linked by both chemicaland electrical (diffusive) synapses. We compare the relative performances of the MATLAB andSIMULINK implementations. Conclusions: The pattern simulations by SIMULINK are in good agreement with theoretical predictions. Comparedwith traditional coding approaches, the SIMULINK block-diagram paradigm reduces the time andprogramming 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 graphicalinterface lends itself to easy modification and use by non-experts.
Electronic ISSN:
1752-0509
Topics:
Biology
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