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

To maintain economic wealth (roads, hospitals, power lines, etc.) power needs to be consumed. The same applies to economic activity, since any activity requires the consumption of energy. According to the Environmental Protection Agency, the burning of fossil fuels was responsible for 79 percent of U.S. greenhouse gas emissions in 2010. So whilst economic activity takes place fossil fuels will be burned and CO2 emissions are unavoidable - unless we use exclusively renewable energy resources, which is not likely to occur very soon. However, the increasing CO2 concentrations in the atmosphere will have negative consequences, such droughts, floods, crop failures, etc. These effects represent limits to economic growth. The CLD illustrates some of the more prominent negative feedback loops that act as a break on economic growth and wealth.  As the negative feedback loops (B1-B4) get stronger, an interesting question is, 'will a sharp reduction in economic wealth and unavoidable recession lead to wide-spread food riots and disturbances?'

Challenge p.212 Business Dynamics, Sterman

Graph representation of Ch3 of their 2007 Monetary Economics book, based on Alvarez and Ehnts 2015 paper The roads not taken. Also see more complex WIP to successively split sectors at IM-185550 . See also essence of MMT IM for simpler intro

Summary WIP of Thomas Palley's 2012 Book

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

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 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.

A simple implementation of a Dynamic ISLM model as proposed by Blanchard (1981), and taken from An introduction to economic Dynamics - Shone (1997) - chapter 5. This model might serve as a framework to evaluate economic policies over GDP growth.

WIP based on Bill mitchell's blogs. 

Implementation of the Solow model of economic growth with labor enhancing technology.

parameters: s, alpha, delta, n, gA
variables: Y. K, L, C, A
per capita variables: y, k, c, a
per capita and technology variables: y~, k~, c~
steady state variables: y~*, k~*, c~*
all variables come with relative growth rates g

Features:

+steady state from beginning
+one time labor shock
+permanent savings quote shock
+permanent technological growth rate shock

Decreasing steady state variables when starting in steady state are numeric artifacts.

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.

Brief Summary of Albert O Hirschman's Book

WIP Ideas from Science Special Issue May 2014

​Farmers use intensive pesticides to harvest cotton, which is harmful to not only the health of the farmers using them, but also our environment as it pollutes rivers and groundwater that negatively interfere with the ecosystem. Even though these farmers know of the health and environmental risks, they still use harmful pesticides to produce cotton, but why is this so. This stock and flow map should explain what impacts farmers to use pesticides to grow cotton despite the risks and explain the cause and effect relationship their use has on the cotton industry and the environment.

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