The Logistic Map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a seminal 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation first created by Pierre François Verhulst. 

Mathematically, the logistic map is written

where:

 is a number between zero and one, and represents the ratio of existing population to the maximum possible population at year n, and hence x0 represents the initial ratio of population to max. population (at year 0)r is a positive number, and represents a combined rate for reproduction and starvation. To generate a bifurcation diagram, set 'r base' to 2 and 'r ramp' to 1
To demonstrate sensitivity to initial conditions, try two runs with 'r base' set to 3 and 'Initial X' of 0.5 and 0.501, then look at first ~20 time steps

Goodwin business cycle model, modified from Keen and Blatt

This is a simplification of the Austerity vs Prosperity model in the hope that it will be easier to understand.

In this Insight I focus on the demand site of the Market and Price model, leaving the supply side out.

Adam Smith's The Invisible Hand: The Feedback Structure of Markets. From Sterman JD Business Dynamics p170 Fig 5-26. A price-mediated resource allocation system..

Adam Smith's The Invisible Hand: The Feedback Structure of Markets. From Sterman JD Business Dynamics p170 Fig 5-26. A price-mediated resource allocation system..

Simple tragedy ​of the commons behavior model.

WIP of Rammelt's 2019 System Dynamics Review Article which has STELLA and Minsky software versions as supplements. Compare with the older IM-2011 version

Investigations into the relationships responsible for the success and failure of nations. This investigation was prompted after reading numerous references on the subject and perceiving that *Why Nations Fail: The Origins of Power, Prosperity, and Poverty* by Acemoglu and Robinson seem to make a great deal of sense.

This model illustrates the current practice and consequences of government spending. Following the direction of the arrows from right to left the model shows the following sequence based on current practice:

Government Spending at a certain point leads to spending in excess of tax receipts. This will automatically lead to the issue of treasuries in the belief that the excess spending must be financed by borrowing (although the government has the capacity to create  money). This in turn will increase the national debt.

 Consequences that follow from this practice:

1) That national debt increases whenever the government spends in excess of tax receipts.

2) That the government must pay interest on the debt issued, which in turn increases and reinforces the need for government spending.

3) That the interest paid on treasuries will increase private sector income.

There is an alternative view, supported by Modern Monetary Theory, of how government spending can proceed. Please see this  Insight: 

https://insightmaker.com/insight/19954

Simplification of Prevention Investment Framework (private) IM See WIP integrating with economic view insight (private) and multiscale version IM private

Adapted from Hartmut Bossel's "System Zoo 3 Simulation Models, Economy, Society, Development."

​Population model where the population is summarized in four age groups (children, parents, older people, old people). Used as a base population model for dealing with issues such as employment, care for the elderly, pensions dynamics, etc.

Adapted from Hartmut Bossel's "System Zoo 3 Simulation Models, Economy, Society, Development."

​Population model where the population is summarized in four age groups (children, parents, older people, old people). Used as a base population model for dealing with issues such as employment, care for the elderly, pensions dynamics, etc.

An initial study of the economics of single use coffee pods.

HANDY Model of Societal Collapse from Ecological Economics Paper 

Sandbox for testing InsightMaker features using pipeline Construction & ROW land conversion as a driver of changes in ecosystem service value.

This model shows the operation of a simple economy. It demonstrates the effect of changes in the fractional rate of consumption (or the converse the fractional rate of saving.)

In summary, lower rates of consumption (based on production) result in higher rates of production and consumption in the long-run.

WIP based on Bill mitchell's blogs

​Climate Sector Boundary Diagram By Guy Lakeman

An initial study of the economics of single use coffee pods.

Regulation of resource allocation to service in response to service quality. A non-price-mediated resource allocation system. From Sterman JD Business Dynamics p172 Fig 5-27

Nutrition and Wellbeing based on 2023 framework from Australian Treasury