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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