The L ogistic 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  Rob

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

This is Figure 6 from Lancastle, N. (2012) 'Circuit Theory Extended: The Role of Speculation in Crises' based on Keen, S. (2010). Solving the Paradox of Monetary Profits.   http://www.economics-ejournal.org/economics/journalarticles/2012-34      Banks expand their lending, which in this model leads
This is Figure 6 from Lancastle, N. (2012) 'Circuit Theory Extended: The Role of Speculation in Crises' based on Keen, S. (2010). Solving the Paradox of Monetary Profits.

http://www.economics-ejournal.org/economics/journalarticles/2012-34

Banks expand their lending, which in this model leads to higher production, wages and spending. The result is an increase in total spending.  
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 l
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.
Clone of Pesticide Use in Central America for Lab work        This model is an attempt to simulate what is commonly referred to as the “pesticide treadmill” in agriculture and how it played out in the cotton industry in Central America after the Second World War until around the 1990s.     The cotto
Clone of Pesticide Use in Central America for Lab work


This model is an attempt to simulate what is commonly referred to as the “pesticide treadmill” in agriculture and how it played out in the cotton industry in Central America after the Second World War until around the 1990s.

The cotton industry expanded dramatically in Central America after WW2, increasing from 20,000 hectares to 463,000 in the late 1970s. This expansion was accompanied by a huge increase in industrial pesticide application which would eventually become the downfall of the industry.

The primary pest for cotton production, bol weevil, became increasingly resistant to chemical pesticides as they were applied each year. The application of pesticides also caused new pests to appear, such as leafworms, cotton aphids and whitefly, which in turn further fuelled increased application of pesticides. 

The treadmill resulted in massive increases in pesticide applications: in the early years they were only applied a few times per season, but this application rose to up to 40 applications per season by the 1970s; accounting for over 50% of the costs of production in some regions. 

The skyrocketing costs associated with increasing pesticide use were one of the key factors that led to the dramatic decline of the cotton industry in Central America: decreasing from its peak in the 1970s to less than 100,000 hectares in the 1990s. “In its wake, economic ruin and environmental devastation were left” as once thriving towns became ghost towns, and once fertile soils were wasted, eroded and abandoned (Lappe, 1998). 

Sources: Douglas L. Murray (1994), Cultivating Crisis: The Human Cost of Pesticides in Latin America, pp35-41; Francis Moore Lappe et al (1998), World Hunger: 12 Myths, 2nd Edition, pp54-55.

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 gre
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.

Original model done for The Perspectives Project though recast into Kumu.
 The L ogistic 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  Rob

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

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
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
Clone of Pesticide Use in Central America for Lab work        This model is an attempt to simulate what is commonly referred to as the “pesticide treadmill” in agriculture and how it played out in the cotton industry in Central America after the Second World War until around the 1990s.     The cotto
Clone of Pesticide Use in Central America for Lab work


This model is an attempt to simulate what is commonly referred to as the “pesticide treadmill” in agriculture and how it played out in the cotton industry in Central America after the Second World War until around the 1990s.

The cotton industry expanded dramatically in Central America after WW2, increasing from 20,000 hectares to 463,000 in the late 1970s. This expansion was accompanied by a huge increase in industrial pesticide application which would eventually become the downfall of the industry.

The primary pest for cotton production, bol weevil, became increasingly resistant to chemical pesticides as they were applied each year. The application of pesticides also caused new pests to appear, such as leafworms, cotton aphids and whitefly, which in turn further fuelled increased application of pesticides. 

The treadmill resulted in massive increases in pesticide applications: in the early years they were only applied a few times per season, but this application rose to up to 40 applications per season by the 1970s; accounting for over 50% of the costs of production in some regions. 

The skyrocketing costs associated with increasing pesticide use were one of the key factors that led to the dramatic decline of the cotton industry in Central America: decreasing from its peak in the 1970s to less than 100,000 hectares in the 1990s. “In its wake, economic ruin and environmental devastation were left” as once thriving towns became ghost towns, and once fertile soils were wasted, eroded and abandoned (Lappe, 1998). 

Sources: Douglas L. Murray (1994), Cultivating Crisis: The Human Cost of Pesticides in Latin America, pp35-41; Francis Moore Lappe et al (1998), World Hunger: 12 Myths, 2nd Edition, pp54-55.

Current and proposed Structure of CCP and related Models expanding on the details provided in the Project Completion plan  IM-101760
Current and proposed Structure of CCP and related Models expanding on the details provided in the Project Completion plan IM-101760
From Bill Mitchell and Warren Mosler December2018 billy  blog entry   and mosler's MMT  white paper  (google docs) 2019. Some highly aggregated stocks and flows and boundaries introduced.
From Bill Mitchell and Warren Mosler December2018 billy blog entry  and mosler's MMT white paper (google docs) 2019. Some highly aggregated stocks and flows and boundaries introduced.
​WIP Summary of 2020  article  Monetary Sovereignty: Nature, Implementation, and Implications by Eric Tymoigne
​WIP Summary of 2020 article Monetary Sovereignty: Nature, Implementation, and Implications by Eric Tymoigne
This is to support a discussion on money flows and growth. Money as a lubricant for the flow of embodied energy in human systems. See also A Prosperous Way Down  website
This is to support a discussion on money flows and growth. Money as a lubricant for the flow of embodied energy in human systems.
See also A Prosperous Way Down website
I made this model to simulate how a companies revenue will change depending on the lifetime of the appliances it manufactures, in combination with the ratio of repair costs and price. It also shows the accumulation of e-waste.
I made this model to simulate how a companies revenue will change depending on the lifetime of the appliances it manufactures, in combination with the ratio of repair costs and price. It also shows the accumulation of e-waste.
Simulation of MTBF with controls   F(t) = 1 - e ^ -λt   Where    • F(t) is the probability of failure    • λ is the failure rate in 1/time unit (1/h, for example)   • t is the observed service life (h, for example)  The inverse curve is the trust time On the right the increase in failures brings its
Simulation of MTBF with controls

F(t) = 1 - e ^ -λt 
Where  
• F(t) is the probability of failure  
• λ is the failure rate in 1/time unit (1/h, for example) 
• t is the observed service life (h, for example)

The inverse curve is the trust time
On the right the increase in failures brings its inverse which is loss of trust and move into suspicion and lack of confidence.
This can be seen in strategic social applications with those who put economy before providing the priorities of the basic living infrastructures for all.

This applies to policies and strategic decisions as well as physical equipment.
A) Equipment wears out through friction and preventive maintenance can increase the useful lifetime, 
B) Policies/working practices/guidelines have to be updated to reflect changes in the external environment and eventually be replaced when for instance a population rises too large (constitutional changes are required to keep pace with evolution, e.g. the concepts of the ancient Greeks, 3000 years ago, who based their thoughts on a small population cannot be applied in 2013 except where populations can be contained into productive working communities with balanced profit and loss centers to ensure sustainability)

Early Life
If we follow the slope from the leftmost start to where it begins to flatten out this can be considered the first period. The first period is characterized by a decreasing failure rate. It is what occurs during the “early life” of a population of units. The weaker units fail leaving a population that is more rigorous.

Useful Life
The next period is the flat bottom portion of the graph. It is called the “useful life” period. Failures occur more in a random sequence during this time. It is difficult to predict which failure mode will occur, but the rate of failures is predictable. Notice the constant slope.  

Wearout
The third period begins at the point where the slope begins to increase and extends to the rightmost end of the graph. This is what happens when units become old and begin to fail at an increasing rate. It is called the “wearout” period. 
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
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.