Small toolbox for simulating reaction diffusion equations of the type
with the diffusion matrix
The space is discretized by finite differences and translated to a big ODE system which is solved using MATLABs ode15s solver.
- Simulation of reaction diffusion equations in one or two spatial dimensions.
- Zeroflux and periodic boundary conditions.
- Easy model setup.
- Spatially dependend parameter possible.
- Import of D2D models (https://github.com/Data2Dynamics)
The model is specified in a .def file in the subfolder /Models of the current MATLAB working directory. The model file is structured like:
STATES
...
EQUATIONS
...
PARAMETERFIELDS
...
The section STATES contains a list of the dynamical states u together with a boolean variable specifying if the state is diffusive. The section EQUATIONS contains a list with the ordinary differential equations (ODEs) defining the reaction part f(u(x,t)) of the reaction diffusion equation f(u(x,t)). The section PARAMETERFIELDS specifies all dynamical parameters which are spatially depend, i.e. k = k(x). See the example Diffusion_from_Source for some use cases.
Please have a look at the examples Diffusion_from_Source and Schnakenberg model to get an idea how to use the code.