Butterfly Effect
Sensitivity To Initial Conditions
(sensitive dependence on initial conditions)
Navier Stokes Equations
Lorenz Attractor
Chaos Theory, Disorder and Entropy



If M is the state space for the map , then  displays sensitive dependence to initial conditions if for any x in M and any δ > 0, there are y in M, with  such that

This model shows the operation of a simple economy with two modifications made to Model 2 -- 1) feedback from production rate to consumption rate and 2) the use of a fractional rate input for calculating consumption rate. 

In summary, lower fractional rates of consumption (based on production) result in higher levels of Savings.

Based on chapter 14 of Modeling Dynamic Economic Systems

This simple model describes wealth accumulation. The value in income is described by the following simple equation:

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.) It also, unlike Models 2 & 3, shows the influence Savings has on the production rate.

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

Irving Fisher's Debt Deflation Theory from Michael Joffe Fig. 3.4 p54 Ch3 Feedback Economics Book with Private Credit Inflation boom added to the  bust cycles

Buying and storing electricity when it is cheap, and selling it when it is expensive. What are the benefits, both public and private?

Causal loop diagram capturing the interactions, trade-offs, and synergies between agriculture (SDG 2), water availability (SDG 6), economic growth (SDG 8), and life on land (SDG 15). Positive feedback linkages are shown as a positive sign (+), whereas negative feedback linkages are shown with a negative sign (−). The purple arrows indicate the enviro-biophysical linkages. The green arrows indicate the socio-economic linkages. The SDG icons are courtesy of the UN SDG communications material. 

Reference - Bandari, Reihaneh, et al. "Participatory Modeling for Analyzing Interactions Between High‐Priority Sustainable Development Goals to Promote Local Sustainability." Earth's Future 11.12 (2023): e2023EF003948.

Peak oil will occur when it is too expensive to bring oil to the surface and not when reserves reach their limit. Companies must make a profit to be able to extract oil and stay in the oil business.  However, that endeavour is becoming more and more difficult because of diminishing returns. They have to dig ever deeper to get to the oil  at ever increasing costs, and the oil they find deep down is of a lesser quality.  We have now reached a point where the price needed by oil companies to make a profit and stay in business is far higher than the price  the market can bear. That price is probably about $ 100 per barrel - and rising every year! A market price o $ 100 will almost certainly cause a sharp recession and cause the price of oil to fall back beyond the point of profitability. For example, the combined profit of ExxonMobile, Chevron and Conocophillips fell from 80.4 billion in 2011 to only 3.7 billon in 2016 - see URL below. What the market can bear depends on the spending power of the mass of non-elite workers. The CLD shows the negative feedback loops that prevent oil prices to rise above the level of  affordability. If non-elite workers cannot afford the goods and services offered,  then there will be no demand for them and by extension for oil.  In this situation the market price will not the cover the cost that oil companies need to extract oil. Oil supplies will decline and so will economic activity!

https://srsroccoreport.com/the-blood-bath-continues-in-the-u-s-major-oil-industry/

Eastern oyster growth model calibrated for Long Island Sound
Developed and implemented by Joao G. Ferreira and Camille Saurel; growth data from Eva Galimany, Gary Wickfors, and Julie Rose; driver data from Julie Rose and Suzanne Bricker; Culture practice from the REServ team and Tessa Getchis. This model is a workbench for combining ecological and economic components for REServ. Economic component added by Trina Wellman.

This is a one box model for an idealized farm with one million oysters seeded (one hectare @ a stocking density of 100 oysters per square meter)

1. Run WinShell individual growth model for one year with Long Island Sound growth drivers;

2. Determine the scope for growth (in dry tissue weight per day) for oysters centered on the five weight classes)
 
3. Apply a classic population dynamics equation:

dn(s,t)/dt = -d[n(s,t)g(s,t)]/ds - u(s)n(s,t)

s: Weight (g)
t: Time
n: Number of individuals of weight s
g: Scope for growth (g day-1)
u: Mortality rate (day-1)

4. Set mortality at 30% per year, slider allows scenarios from 30% to 80% per year

5. Determine harvestable biomass, i.e. weight class 5, 40-50 g (roughly three inches length)

Challenge p.212 Business Dynamics, Sterman

Based on the Market and Price simulation model in System Zoo 3.

Any activity  requires the use of energy. Economic activity is not possible without energy,  especially fossil fuels. An increase in economic activity necessarily leads to an increase in the use  fossil fuels and greenhouse gas emissions. In addition there will   be a commensurate increase in waste products, pollution and heat. This is dictated by the laws of physics and unavoidable.  A problem arise when the cost of this degeneration caused by continual economic growth surpasses the benefit society derives from it. The ecological economist Professor Herman Daly (2014) explained that when the impact on the ecosystem is correctly measured, global growth has reached a point where the total private and social costs of economic growth outweigh the private and social benefits. In other words, more economic growth is making global society worse off overall - growth has become uneconomic! The model shows that eventually pressures will build up that counteract the perennial belief that all social ills can be solved with economic growth. 

This model analyzes the interaction between climate change mitigation and adaptation in the land use sector using the concept of forest transition as a framework.

How long would it take for a digital health innovation to be sustained after implementation

WIP Ideas from Science Special Issue May 2014

This model shows the operation of an extremely simple economy. The system produces and consumes each item (or good) at a fixed rate.

When production exceeds consumption, consumer goods accumulate in stocks. Trading may occur between actors in this system. That will not, however, affect the quantities of the stocks of goods. It only affects ownership (not a concern of this model.)

Extended from Im-628 Supply and demand by adding control folder.

ABOUT THE MODEL

This is a dynamic model that shows the correlation between the health-related policies implemented by the Government in response to COVID-19 outbreak in Burnie, Tasmania, and the policies’ impact on the Economic activity of the area.

 ASSUMPTIONS

The increase in the number of COVID-19 cases is directly proportional to the increase in the Government policies in the infected region. The Government policies negatively impact the economy of Burnie, Tasmania.

INTERESTING INSIGHTS

1. When the borders are closed by the government, the economy is severely affected by the decrease of revenue generated by the Civil aviation/Migration rate. As the number of COVID-19 cases increase, the number of people allowed to enter Australian borders will also decrease by the government. 

2. The Economic activity sharply increases and stays in uniformity. 

3. The death rate drastically decreased as we increased test rate by 90%.