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System Dynamics Models

System Dynamics is a powerful approach for modeling change within systems and Insight Maker is perfect for building System Dynamics models.

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Explore What Others Are Building

Here is a sample of public Insights made by Insight Maker users. This list is auto-generated and updated daily.

The Lotka-Volterra equations (also known as the predator-prey equations) model the dynamic interactions between two biological populations: a predator and its prey.

This form of modeling dynamic systems is based on "stocks" (amounts) and "flows" (rates of change). For the predator-prey model we ask what factors impact the flows (the thick arrows) into and out of the populations of sheep and wolves (the stocks)? The dotted arrows can be used to connect and describe the relationships within the model. Additional variables, e.g, sheep fertility, can be added to the model to make relations clearer.

Overall, the dynamics for this kind of modeling centers on the factors that impact the flows. Click on any of the flow-arrows to see how the factors connect by the dotted arrows are used to determine the flows in or out of the stocks (the populations).

Wreski_Lab2_predatorPrey

maddox wreski

4 days ago

Unfolding WIP of Eric Wolstenholme's explanation of hospital congestion from March 2022 Youtube video and online stella presentation. Use of cascading interlinked archetypes. See Kumu version, early discharge boundaries IM for an earlier version and Generic Archetypes IM from Gene and Simpler Version IM

Hospital congestion cascading archetypes

Geoff McDonnell

From Jay Forrester 1971 book World Dynamics, the earlier, simpler version of the World 3 Limits to Growth Model. Adapted by Geoff McDonnell from Mark Heffernan's ithink version at Systemswiki.org.

@LinkedIn, Twitter, YouTube

World2 Model of World Dynamics

Gene Bellinger

This (simplest!) model demonstrates logistic growth.The original differential equation looks like

y'(t) = b y(t) (1 - y(t)/K)

where K is the carrying capacity of the quantity y.

But if we divide each side of the equation by K, we obtain

d(y/K)/dt = b (y/K) (1-y/K)

Defining a new variable w, the population relative to its carrying capacity, we obtain

dw/dt = b w (1 - w)

Finally we divide both sides by b, to write

dw/d(bt) = w (1 - w)

So if we work in dimensionless time units of bt, we have

w' = w (1 - w)

where the derivative is with respect to the variable bt=τ. .

τ=τ

This

This equation, as simple as possible, contains all the dynamics (all the ways the population can behave), while masking the "trivialities"; but it kind of hides the physical aspects of the problem. So it's easy to study, but harder to interpret: alas, you can't have it all!:)

τ=1 when t=1b: so if b=.5/year, then τ=1 when t=2.

So the larger b (the greater the birthrate), the shorter the real time t to give τ=1.

τ=τ=

τ=

Non-dimensionalized Logistic Growth

Andrew E Long

Food Waste and Carbon Emissions

Evelyn Huang

This model compares exponential growth vs logistic growth of a Quokka population. Quokka's are a small creature which are native to the Australian continent. This population increases due to addition of joey's that enter the initial quokka population through each quokka mother that gives birth. The loss of numbers is the quokka's leaving the population by death. This whole system keeps the quokka population in equilibrium and can also act as a guide to sustainability, as it allows us to view birth and death rates of a population. We can then work with the numbers of this model to decide how we want to approach this population with sustainability in mind. For example, a high birth rate means we would need to find methods to control the population to create a sustainable environment which is able to maintain this population.

The second version of the model introduces the concept of a Carrying Capacity and uses "logistic" growth formula, which "caps" the population - this is representing resource limitation.

Quokkas on an Island

Matt Hipsey

23 last month