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.
For approximate Continuous Behavior set 'R Base' to a small number like 0.125To 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

Spending by the government creates its own 'financial resource' as the process of crediting an account in the private sector takes place. This may sound like nonsense, but in fact it is 'monetary reality'. This premise is supported by Bell (1998; 2000) and Wray (1998a) who argue that the Treasury does not need to collect or borrow funds in order to spend, but crates new funds as it spends.

Perhaps the following thought experiment  helps to understand how this is possible.  

If you imagine two drawers, each representing an account. The first drawer contains 100 gold coins and the second is empty. Also imagine that there are no other gold coins available at this time. Let's call the first drawer account A and the second account B. Now if you want to transfer 30 gold coins from account A to account B, you would actually first have to take the coins out of drawer A and then place them into drawer B. Account A will then necessarily have 30 coins less in it. Now imagine accounts A and B are held in a computer as electronic money. Instead of 100 gold coins, account A only contains the computer generated number '100'  and account B shows '0'. To get account B to show a balance of '30', it would now simple be necessary to change the '0' to '30' on the computer. The need to raid account A and to take '30' from the number '100' before you could credit  account B does not exist. Money is created as it is entered in B's account irrespective of whether A's account is debited before or after this process or not at

WIP based on Bill mitchell's blogs. 

CLD exposition of Goodwin01 from Steve Keen's August 2019 course on Introduction to Economic Dynamics and Minsky software See video and powerpoint slides. Based on IM-2011 Minsky FIH and IM-168865 MacroEconomics CLDs. SeeIM-172005 for Simulation

WIP Ideas from Science Special Issue May 2014

Simulation of Goodwin01 Minsky Model CLD in IM-172002 Compare with Part3 slide 3 of presentation in patreon. See extension Goodwin02 at IM-172145

I propose we grow this sim model (or similar) over time to help ourselves better understand the opposing investment and austerity strategies now being advocated for the U.S. government. The hope is to build as simple a model as possible that subsumes the major underlying feedback loops that probably exist in the mental models of proponents of each of these positions. Starting this model was inspired by this Investment vs. Austerity discussion http://www.linkedin.com/groups/Investment-vs-Austerity-How-can-4582801.S.157876413

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.

Unfortunately, this model only produces the illusion of functioning, but I did manage to get it to give me the graph. However, because of the use of flows, if you change the time step to and the simulation length to anything other than the same numbers, you'll find the graph showing something that looks more exponential. This is due to the function referencing itself in regards to time, so inevitably each time consumption grows it changes the outcome on the other side of the equation. Still, this is a convincing mock up. I added a "45 degree" line so that one could conceivably see (and also change) the difference made by altering the level of autonomous consumption.

WIP Overview model structures of Khalid Saeed's 2014 WPI paper Jay Forrester’s Disruptive Models of Economic Behavior  See also General SD and Macroeconomics CLDs IM-168865

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

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.

Stock-flow diagram of compound interest with table and graph output in interest and savings development per year in Dutch. With the possibility of a negative interest from a predefined threshold.

This is an important Henry George insight; labor creates all wealth (rather than capital creating it).

Circular equations WIP for Runy.

WIP Elements from macroeconomics, neoliberalism and commercial determinants of health frameworks to provide a background to the effects of the universal basic income on health and wellbeing for the first 1000 days. UBI diagram modified from Johnson2021 article Expanded in Insight 2

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..

Like previous models, this model shows the operation of a simple economy, the influence of changes in the consumption rate, and the effect of government intervention. In addition, this model shows changes in the hypothetical general price level. It gives an idea of changes in price trends based on changes in the quantity of money. NOTE: No general price level exists. Prices provide information for the exchange of individual economic goods.

Here I've translated the macoreconomic rule 'SPENDING = INCOME = OUTPUT, WHICH DRIVES EMPLOYMENT' into a negative feedback loop by adding an explicit goal of Output and Employment. As shown in 'Investment and Output 1', all the income earned has to be spent to maintain output and employment. Any shorfall in spending can be made up by any of the three sectors that contribute to total output. However, when spending/investment by the private sector is too small to maintain the required level of overall spending and the exports do not contribute enough to compensate for this shortfall then only the government can save the day through Net Spending, i.e. spending more than it collects in tax revenue. Taxation at any rate, according to Modern Monetary Theory (MMT) does not serve the purpose of financing spending but can be used legitimately to slow down an overheating economy. I have not taken into account 'structural reforms', which are often subject to the 'Fallacy of Composition' and of dubious value, at least in a recessive climate, according to MMT.

Addition to Program Evaluation Insight based on Health System Efficiency WHO Europe 2016 publication includes vital signs

From Jay Forrester 1988 killian lectures youtube video describing system dynamics at MIT. For more detailed biography See Jay Forrester memorial webpage For MIT HIstory see IM-184930 For Applications se IM-185462

There is an old saying that says that 'opportunity makes thieves'.  But there is  also a research paper entitled 'Opportunity makes the Thief: Practical Theory of Crime Prevention (1998)' that provides evidence supporting this common observation. The paper argues that  opportunity is a “root cause” of crime. This therefore also applies to the behaviour of corporations.

 

The Causal Loop Diagram on the left indicates that the number of crimes will  increase rapidly as the opportunities to commit them increases.  This suggests that the introduction of a negative feedback loop aimed at diminishing  opportunities for committing crimes is an appropriate measure to improve the situation. A number of remedial mesures  tailored to specific situations are contained in the report. A generally effective means must be the use of law and regulations that were also mentioned in the report.