 Projects/ISLE/Concepts

# Equation

SC-IPM's Generic Process specifications use equations to define the behavior of the processes being modeled. So, for example, a Generic Process might use:

## Algebraic Equations

SC-IPM uses algebraic (ie, static) equations, along with pre-defined aggregators (eg, `prod`, `sum`), to model instantaneous relationships. For example, the total predation rate might be defined as the `sum` of a set of (more specific) predation models.

## Differential Equations

SC-IPM uses differential equations to model processes that involve change over time. For example, the rate of growth or loss in a process's output variable (eg, population) might depend on the values of parameters and/or other variables.

### Ordinary Differential Equations

Ordinary Differential Equations (ODEs) only range over a single input variable (eg, population with respect to time). At the moment, SC-IPM only supports ODEs: a set of input parameters and variables is mapped to an output variable with respect to time.

Bret Victor has created a very intriguing video, showing a possible way to visualize (and interact with) ODEs. Conveniently, he uses the predator-prey model as his main example.

### Partial Differential Equations

Partial Differential Equations (PDEs) can range over more than one input variable (eg, time and depth in an aquatic ecosystem). Supporting PDEs would allow SC-IPM to handle a wider range of modeling tasks.

It would also allow SC-IPM to handle some current tasks in a cleaner and more effective manner. For example, "depth" could be an important variable in an aquatic ecosystem model. An approximation of a PDE can be modeled using an ODE for each of several strata (ie, depth ranges). However, this workaround fails when:

• the process isn't based on time

• finer granularity is required

• many input variables are needed

## Resources

This wiki page is maintained by Rich Morin, an independent consultant specializing in software design, development, and documentation. Please feel free to email comments, inquiries, suggestions, etc!

Topic revision: r4 - 26 Jul 2013, RichMorin
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