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

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

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

HANDY Model of Societal Collapse from Ecological Economics Paper 

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

Summary of Zimmerman2013 article (paywalled) Habit, custom, and power: A multi-level theory of population health. Also mapped to COM-B. See also Dynamics in action IM, PCT Double Loop Learning IM and Structure Agency framework IM

Simulating Hyperinflation for 3650 days.

If private bond holdings are going down and the government is running a big deficit then the central bank has to monetize bonds equal to the deficit plus the decrease in private bond holdings.  We don't show the details of the central bank buying bonds here, just the net results.

See blog at http://howfiatdies.blogspot.com for more on hyperinflation, including a hyperinflation FAQ.

Nutrition and Wellbeing based on 2023 framework from Australian Treasury

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

Goodwin business cycle model, modified from Keen and Blatt

Goodwin business cycle model, modified from Keen and Blatt

Very basic stock-flow diagram of compound interest with table and graph output in interest and savings development per year. Initial deposit, interest rate, yearly deposit and withdrawal can all be modified.

Simple tragedy ​of the commons behavior model.

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

During the 'big recession' many governments have deliberately repressed salaries, usually via structural reforms, in order to gain competitivity. However, repression of salaries increases inequality, social discontent and often has counterintuitive effects. Salaries are a cost for companies, but they are also the basis for the demand for the goods and services they offer: people with little income cannot afford them. Scientific studies have shown repeatedly that economic growth generated via salary increases does not endanger the creation of employment, but rather reinforces it. In most countries, the 'positive effect of salary increases' eclipses any possible negative effects on export competitivity and even any detrimental effect on investment. A good example of such a study is the work of ONARAN and OBST on Wage-led Growth in the EU15 Member States (2016).  This positive dynamic has been highlighted in the model by prominent arrows. The policy implications for governments are clear! 

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.

THE NEW SCIENCE OF PLEASURE Daniel L. McFadden NBER Working Paper 18687

THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION

The existing global capitalistic growth paradigm is totally flawed

Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of unpredictable chaotic turbulence puts the controls ito a situation that will never return the system to its initial conditions as it is STIC system (Lorenz)

The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite working containers (villages communities)

Goodwin cycle IM-2010 with debt and taxes added, modified from Steve Keen's illustration of Hyman Minsky's Financial Instability Hypothesis "stability begets instability". This can be extended by adding the Ponzi effect of borrowing for speculative investment.

This model compares direct exchange prices to money prices. It demonstrates the distortion that monetary expansion or contraction has on the information contained in monetary pricing.

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

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.