Simulistics

At heart, many Systems Dynamics models consist of differential equations, each one represented by a compartment / flow structure, though you don’t need to know this to set up the model. On the other hand, if you’re given the differential equations, it is very straightforward to enter these into the model.

For example, given the differential equation:

dx/dt = x/20 - x²/2000

you know two things:

This section focuses on how to express mathematical expressions in Simile as diagram symbols and an expression in Simile.

This is one of the most common constructions. The rate of change of the state variable is a function of its present value.

This section deals with arrangements of diagram elements to achieve certain goals.

The aim of this section is to introduce you to a number of compartment-flow modelling building blocks that you can incorporate into your own modelling. Most of these relate to the inclusion of exogenous variables — externally-varying factors such as temperature or rainfall — in your model.

These five examples have demonstrated a number of important points.

The above examples all share one thing in common: they represent a population in terms of the values for one or more state variables, there being as many state variables as there are classes in the population. Each state variable may be engineered to have integer values (on the basis that populations contain a discrete number of individuals), or to have real (floating point) values, if you are content to think in terms of population density (i.e. number per unit area) rather than absolute numbers.

The previous method is a big improvement: it is a much more concise way of representing multiple age classes, and exactly the same model can be used regardless of the number of classes we have: in other words, it scales up to larger problems. However, it suffers from a couple of disadvantages:

The above two examples are expressed in conventional System Dynamics terms. They set the scene for the next three, which are now expressed in terms unique to Simile.

The same population is now represented by four compartments, one for each of four age classes. The first one represents the first year group, the second represents the number of animals aged 1-5 inclusive, the next animals aged 6-15 inclusive, and the fourth for all remaining animals. As before, the mortality rate per animal is independent of population size, but now depends on its age (there is a different m value for each age class). The reproductive rate per individual is still influenced by total population size, as well as now being different for each age class.