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

 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 5 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      Households are given a direct, monetary boost. Higher
This is Figure 5 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

Households are given a direct, monetary boost. Higher spending leads to greater investment in production, and a rise in total spending. 
Book Summary of The Great Transformation by Karl Polanyi see  Wikipedia  . See also more Karl Polanyi ideas  IM-181325
Book Summary of The Great Transformation by Karl Polanyi see Wikipedia . See also more Karl Polanyi ideas IM-181325
 Nobody seems to notice bubbles until they burst. One possible reason is that those caught up in a bubble are completely blinded by the grip, the overpowering logic and force  excerted by the positive feedback loop that drives it. Financial bubbles occur time and time again - and nobody seems to lea

Nobody seems to notice bubbles until they burst. One possible reason is that those caught up in a bubble are completely blinded by the grip, the overpowering logic and force excerted by the positive feedback loop that drives it. Financial bubbles occur time and time again - and nobody seems to learn. Another example on a different time scale is an argument that spins out of control and ends in violence. The participants seem to be blind to the consequences; the immediate and imperative logic of the feedback loop imposes itself. The vortex created by the feedback loop even seems to draw in outsiders, such as new investors. Is this the reason why we don't notice bubbles? This explanation is meant to stimulate discussion!

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.

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 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
 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..

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..

The upper
diagram shows the principal factors that have an influence on the budget
deficit and indicates what needs to be done to correct it. But this is not the
full story. The diagram below shows that 
cutting public expenditure reduces aggregate demand and  increases unemployment. The reduction o
The upper diagram shows the principal factors that have an influence on the budget deficit and indicates what needs to be done to correct it. But this is not the full story. The diagram below shows that  cutting public expenditure reduces aggregate demand and  increases unemployment. The reduction of aggregate demand  reduces  economic activity which has the effect of reducing  tax revenue.  In addition, the state has to pay out funds as there is a need for more unemployment benefit payments.   The result of these austerity measures  is often the opposite of their intended purpose: they can increase rather than decrease the budget deficit.

There is plenty of empiric evidence to show that this has happened time and time again. For instance, a report from UNCTAD (United Nations Conference on Trade and Development) found that between 1990 and 2000 in all the  cases examined where cutbacks in public spending and tax increases were used, the fiscal situation did not only not improve but worsened. Despite such repeated evidence, unfortunately calls for  austerity measures continue to be heard. 

Taken from Saeed, Khalid. ‘Limits to Growth Concepts in Classical Economics’. In  Feedback Economics: Economic Modeling with System Dynamics , edited by Robert Y. Cavana, Brian C. Dangerfield, Oleg V. Pavlov, Michael J. Radzicki, and I. David Wheat, 217–46. Cham: Springer International Publishing, 2
Taken from Saeed, Khalid. ‘Limits to Growth Concepts in Classical Economics’. In Feedback Economics: Economic Modeling with System Dynamics, edited by Robert Y. Cavana, Brian C. Dangerfield, Oleg V. Pavlov, Michael J. Radzicki, and I. David Wheat, 217–46. Cham: Springer International Publishing, 2021. https://doi.org/10.1007/978-3-030-67190-7_9.

Note that I haven't been able to reproduce the reported results!
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,
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.
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.

Extended from  Im-628  Supply and demand by adding control folder. See also Managing Health Services Use  IM-17566   Based on JHPPL 2015  article  Note here the framing is an economic exchange rather than a public service (needs-services-resources) or capabilities
Extended from Im-628 Supply and demand by adding control folder.
See also Managing Health Services Use IM-17566
Based on JHPPL 2015 article Note here the framing is an economic exchange rather than a public service (needs-services-resources) or capabilities
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,
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.
 
			 
				 
					 From Oatley 2014 p214++   Balance-of-Payments Adjustment
  
					 Even though the current and capital accounts must balance each other, there
is no assurancethat the millions of international transactions that individu-
als, businesses, and governments conduct every year will nece

From Oatley 2014 p214++

Balance-of-Payments Adjustment

Even though the current and capital accounts must balance each other, there is no assurancethat the millions of international transactions that individu- als, businesses, and governments conduct every year will necessarily produce this balance. When they don’t, the country faces an imbalance of payments. A country might have a current-accountdeficit that it cannotfully finance throughcapital imports, for example, or it might have a current-accountsur- plus thatis not fully offset by capital outflows. When an imbalancearises, the country must bring its payments back into balance. The process by which a country doessois called balance-of-payments adjustment. Fixed and floating exchange-rate systems adjust imbalances indifferent ways.

In a fixed exchange-rate system, balance-of-payments adjustment occurs through changes in domestic prices. We can most readily understand this ad- justmentprocess through a simple example. Suppose there are only two coun- tries in the world—the United States and Japan—and supposefurther that they maintain a fixed exchange rate according to which $1 equals 100 yen. The United States has purchased 800 billion yen worth of goods, services, and financial assets from Japan, and Japanhas purchased $4 billion of items from the United States. Thus, the United States has a deficit, and Japan a surplus, of $4billion. 

This payments imbalance creates an imbalance between the supply of and the demandfor the dollar and yen in the foreign exchange market. American residents need 800 billion yen to pay for their imports from Japan. They can acquirethis 800 billion yen by selling $8 billion. Japanese residents need only $4 billion to pay for their imports from the United States. They can acquire the $4 billion by selling 400billion yen. Thus, Americanresidentsareselling $4 billion more than Japanese residents want to buy, and the dollar depreci- ates againstthe yen.

Because the exchangerateis fixed, the United States and Japan must prevent this depreciation. Thus, both governmentsintervenein the foreign exchange market, buying dollars in exchange for yen. Intervention has two consequences.First, it eliminates the imbalance in the foreign exchange mar- ket as the governments provide the 400billion yen that American residents need in exchange forthe $4 billion that Japanese residents do not want. With the supply of each currency equalto the demandin the foreign exchange mar- ket, the fixed exchangerate is sustained. Second, intervention changes each country’s money supply. The American moneysupply falls by $4 billion, and Japan’s moneysupplyincreases by 400billion yen. 

The change in the money supplies alters prices in both countries. The reduc- tion of the U.S. money supply causes Americanpricesto fall. The expansion of the money supply in Japan causes Japanese prices to rise. As American prices fall and Japanese prices rise, American goods becomerelatively less expensive than Japanese goods. Consequently, American and Japaneseresidents shift their purchases away from Japanese products and toward American goods. American imports (and hence Japanese exports) fall, and American exports (and hence Japanese imports) rise. As American imports (and Japanese exports) fall and American exports (and Japanese imports) rise, the payments imbalanceis elimi- nated. Adjustment underfixed exchange rates thus occurs through changesin the relative price of American and Japanese goods brought about by the changes in moneysupplies caused by intervention in the foreign exchange market.

In floating exchange-rate systems, balance-of-payments adjustment oc- curs through exchange-rate movements. Let’s go back to our U.S.—Japan sce- nario, keeping everything the same, exceptthis time allowing the currencies to float rather than requiring the governments to maintain a fixed exchangerate. Again,the $4 billion payments imbalance generates an imbalancein the for- eign exchange market: Americansare selling more dollars than Japanese resi- dents want to buy. Consequently, the dollar begins to depreciate against the yen. Because the currencies are floating, however, neither governmentinter- venesin the foreign exchange market. Instead, the dollar depreciates until the marketclears. In essence, as Americans seek the yen they need, they are forced to accept fewer yen for each dollar. Eventually, however, they will acquire all of the yen they need, but will have paid more than $4 billion for them.

The dollar’s depreciation lowers the price in yen of American goods and services in the Japanese market andraises the price in dollars of Japanese goodsandservices in the American market. A 10 percent devaluation of the dollar against the yen, for example, reduces the price that Japanese residents pay for American goods by 10 percentandraises the price that Americans pay for Japanese goods by 10 percent. By making American products cheaper and Japanese goods more expensive, depreciation causes American imports from Japan to fall and American exports to Japan to rise. As American exports expand and importsfall, the payments imbalanceis corrected.

In both systems, therefore, a balance-of-payments adjustment occurs as prices fall in the country with the deficit and rise in the country with the surplus. Consumers in both countries respond to these price changes by purchasing fewer of the now-more-expensive goods in the country with the surplus and more of the now-cheaper goodsin the country with the deficit. These shifts in consumption alter imports and exports in both countries, mov- ing each of their payments back into balance. The mechanism that causes these price changes is different in each system, however. In fixed exchange- rate systems, the exchange rate remains stable and price changes are achieved by changing the moneysupplyin orderto alter prices inside the country. In floating exchange-rate systems, internal prices remain stable, while the change in relative prices is brought about through exchange-rate movements.

Contrasting the balance of payments adjustment process under fixed and floating exchangerates highlights the trade off that governments face between

exchangerate stability and domestic price stability: Governments can have a stable fixed exchangerate or they can stabilize domestic prices, but they cannotachieve both goals simultaneously. If a government wants to maintain a fixed exchangerate, it must accept the occasional deflation and inflation caused by balance-of-payments adjustment. If a governmentis unwilling to accept such price movements,it cannot maintain a fixed exchangerate. This trade-off has been the central factor driving the international monetary system toward floating exchange rates during the last 100 years. We turn now to examine howthis trade-off first led governmentsto create innovativeinter- national monetary arrangements following World WarII and then caused the system to collapse into a floating exchange-rate system in the early 1970s. 

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.