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 writtenwhere:
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
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.
The complex model reflects the COVID-19 outbreak in Burnie, Tasmania. The model explains how the COVID-19 outbreak will influence the government policies and economic impacts. The infected population will be based on how many susceptible, infected, and recovered individuals in Burnie. It influences the probability of infected population meeting with susceptible individuals.
The fatality rate will be influenced by the elderly population and pre-existing medical conditions. Even though individuals can recover from COVID-19 disease, some of them will have immunity loss and become part of the susceptible individuals, or they will be diagnosed with long term illnesses (mental and physical). Thus, these variables influence the number of confirmed cases in Burnie and the implementation of government policies.
The government policies depend on the confirmed COVID-19 cases. The government policies include business restrictions, lock down, vaccination and testing rate. These variables have negative impacts on the infection of COVID-19 disease. However, these policies have some negative effects on commercial industry and positive effects on e-commerce and medical industry. These businesses growth rate can influence the economic growth of Burnie with the economic
Most of the variables are adjustable with the slider provided below. They can be adjusted from 0 to 1, which illustrates the percentages associated with the specific variables. They can also be adjusted to three decimal points, i.e., from 0.1 to 0.001.
Assumptions
- The maximum
population of Burnie is 20000.
- The maximum
number of infected individuals is 100.
- Government
policies are triggered when the COVID-19 cases reach 10 or above.
- The government
policies include business restrictions, lock down, vaccination and testing
rates only. Other policies are not being considered under this model.
- The vaccination
policy implemented by the government is compulsory.
- The testing
rate is set by the government. The slider should not be changed unless the testing
rate is adjusted by the government.
- The
fatality rate is influenced by the elderly population and pre-existing medical
conditions only. Other factors are not being considered under this model.
- People who
recovered from COVID-19 disease will definitely suffer form immunity loss or any
other long term illnesses.
- Long term
illnesses include mental illnesses and physical illnesses only. Other illnesses
are not being considered under this model.
- Economic activities
are provided with an assumption value of 1000.
- The higher
the number of COVID-19 cases, the more negative impact they have on the economy
of Burnie.
Interesting Insights
A higher recovery rate can decrease the number of COVID-19 cases as well as the probability of infected population meeting with susceptible persons, but it takes longer for the economy to recover compared to a lower recovery rate. A higher recovery rate can generate a larger number of people diagnosed with long term illnesses.
Testing rate triggers multiple variables, such as government policies, positive cases, susceptible and infected individuals. A lower testing rate can decrease the COVID-19 confirmed cases, but it can increase the number of susceptible people. And a higher testing rate can trigger the implementation of government policies, thus decreasing the infection rate. As the testing rate has a strong correlation with the government policies, it can also influence the economy of Burnie.
Clone of Wagdy Samir Macroeconomics work in progress IM-901 Additions and deletions based on Robert Skidelsky's description of Keynes general THeory from his Biography Vol2 p 549 -571
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..
Assignment 3 – Complex Systems
Ryan Salvaggio - 43668070
The Model
This model conceptualizes the effects on a real-estate market-model utilizing agent based modelling. This model utilizes basic economic principles of supply and demand.
The model bases itself on two Agents - one being ‘Customers’ of the real estate market model, whilst the other being the Real estate itself, coined 'Houses'.
Consumers (Demand)
The Agent population, ‘Consumers’ specifies the total amount of people whom can potentially become buyers within the market. This is limited to 30 for conceptual purposes. The Agent ‘Consumer’ exists in two states, either being an ‘Active Customer’ (Active) or an ‘Inactive Customer’ (Inactive). The transition from Inactive to Active occurs upon the basis that the ‘Budget’ of the Consumer meets the desired price of the marketplace, this is specified through the variable ‘Budget’ defining the probability that this transition will occur – this is adjustable by the user indicating a highly resistive or by accepting the market. ‘Budget’s probability in a real life scenario would be based upon numerous factors however conceptually utilizing the slider can present many of these various situations.
Upon transitioning into an active state an ‘Active consumer’ will attempt to find the closest ‘For sale household’, this is represented and carried out through the ‘Enter’ action. Upon finding a household the consumer and house will both return to their respected inactive state thus repeating the process.
Demand – ‘Count of active customers – demand’ is then calculated by a count of Consumers transitioned and currently in the Active state. A high demand would be indicative through a high ‘Budget’ responsiveness whilst a low demand would be indicative of a low ‘Budget’ responsiveness. The increase in Price and hence supply of household thus reduces demand and vise versa.
House (Supply)
The Agent population, ‘Houses’ specifies the total amount of households that can potentially become for sale within the market. This is limited to 112 for conceptual purposes. The Agent ‘House’ exists in two states, either being ‘For Sale’ (Active) or ‘Not for Sale’ (Inactive). The transition from Inactive to Active occurs upon the basis that the ‘Motivation to Sell’ of the House is satisfied, this satisfaction is specified by a set probability that this transition will occur – this is adjustable by the user indicating a highly responsive or restricted house market. ‘Motivation to sell’ probability in a real life scenario would be based upon numerous factors however conceptually utilizing the slider can present many of these various situations.
Upon transitioning into an active state a ‘For Sale’ house will wait for an ‘Active Customer’ ‘this is represented and carried out through the ‘Search’ action. Upon completion of the action both states become inactive and the process continues.
Supply – ‘Count of houses for sale –supply’ is then calculated by a count of Houses ‘For Sale’ that are currently in the active state. Ultimately a high Motivation to sell would sharply increase supply, whilst a low motivation would have the adverse effects.
Movement Speed
Movement speed – describes the base movement rate of Consumers. This variable describes the transition into the ‘Inactive’ state of a consumer, ultimately when a household is found and purchased. Movement speed affects both demand and supply in the sense that the transitioning of stages is quickened and more responsive. (Indicated by a more rigid demand and supply curve).
Market Price
In economics Price is a linear function (straight line) of the proportion of houses for sale (positive slope), and also a linear function of the proportion of buyers (negative slope).Therefore , the variable ‘Market Price’ is calculated by 10 * the portion of ‘House’ in the active state (which is the supply) over the portion of ‘Consumers’ in the active state (which is the demand) Ultimately this presents the economic principles that as Supply is directly related to Price and demand is inversely related to Price.
Note
Each simulation (with the same settings) will present a different and unique simulation. I have set a Random Boolean to the active component that randomizes the amount of Customers or houses that begin in their active state. The probability is only 0.008 but is useful in describing the effects on the market from various position’s and seeing unique models.
References
https://www.youtube.com/watch?v=ynuoZQbqeUg - Your First ABM/Part II
https://insightmaker.com/insight/35714/Foraging-Model
The recent moratorium on deep-sea drilling will reduce the supply of oil. But the world-wide trend is an ever increasing demand for it. This simple CLD tries to illustrate the dampening effect on demand and on economic activity of diminishing oil supplies and of rising prices: oil prices affect virtually all products and especially agricultural production. As it becomes more and more difficult to extract oil, prices must rise. At the moment the global recession counteracts this effect, but the recession will not last forever. Is it too early to speak of Peak Oil?
