StochSD[1] (Stochastic System Dynamics) is a free, open-source Continuous System Simulation (CSS) package intended for small and medium-sized models in education, self-studies and research.

Technically, StochSD is based on the Insight Maker[2] engine with its DE-solver, function library, error checker, macro facility, etc., while the design, graphical user's interface, construction elements, result presentation, file handling, link checking, etc.

Also, tools for sensitivity analysis, and optimisation with or without constraints are included.

In particular, StochSD includes features for stochastic modelling, post-analysis of multiple simulations, and presentation of the results in statistical form.

This course material contains lectures, laboratory exercises, instructive models, and StochSD manuals, which mainly are based on material developed at Uppsala University and the Swedish University of Agricultural Sciences for courses in modelling and simulation.

StochSD is downloaded in many countries from all continents,[11] and can also be run directly in a web browser (of which there is no statistics).

It is described, compared and discussed,[12][13][14][15][16] demonstrated in educational videos,[17][18][19] and also referred to in various languages.

[20][21][22] The Full Potential CSS concept is an extension of classical Continuous System Simulation, which provides the rules to make the results from macro-modelling consistent with those from micro-modelling.

[6][7][8][9] Briefly, in addition to modelling and simulating continuous flows between stocks represented by ‘real numbers’, StochSD can also handle transitions of discrete entities by integer numbers.

[6] However, such transitions may happen irregularly over time, so stochasticity often plays a crucial role in their modelling.

Therefore, StochSD contains powerful random functions to model uncertainties of different kinds, as well as devices to collect statistics during a simulation and from multiple replications of the same stochastic model.

The Full Potential concept also includes rules for how a stage has to be expanded into a structure of stocks and flows in order to reproduce a specific sojourn-time distribution, how attributes are to be handled, and where and how different types of uncertainty (structural, transition, initial value, parameter, and signal uncertainties) should be implemented.

Now assume that the births and deaths of the sheep are discrete random events with the expected rate d⋅X⋅Y and e⋅Y, respectively, then the number of events per time interval is Poisson distributed.

The StochSD function PoFlow(expected_value) handles this by drawing a random number for each DT.

The modifications to obtain a combined model are shown in red, below.

In the replication shown, the discrete predators became extinct at around 235 time units (e.g., months).

The continuous prey then increases logistically to an equilibrium without further stochastic variations.

The traditional alternative of constructing a combined continuous and discrete model, with its mixture of disparate DES and CSS concepts, synchronisation of two different time-handling methods, and requiring a special combined simulation language is not an attractive option for a macro study.