The World3 Model: A Detailed World Forecaster
Isle Royale: Predator Prey Interactions
Cane Toad Food Web
Cats Over Borneo Food Chain
Phyto 2 - Michaelis-Menten curve for phytoplankton
The equation is:
P = Ppot S / (Ks + S)
P: Nutrient-limited production (e.g. d-1, or mg C m-2 d-1)
Ppot: Potential production (same units as P)
S: Nutrient concentation (e.g. umol N L-1)
Ks: Half saturation constant for nutrient (same units as S)
The model contains no state variables, just illustrates the rate of production, by making the value of S equal to the timestep (in days). Move the slider to the left for more pronounced hyperbolic response, to the right for linear response.
THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES CHAOTIC TURBULENCE (+controls)
The existing global capitalistic growth paradigm is totally flawed
Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of unpredictable chaotic turbulence puts the controls ito a situation that will never return the system to its initial conditions as it is STIC system (Lorenz)
The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks
See Guy Lakeman Bubble Theory for more details on keeping systems within finite working containers (villages communities)
NPD model (Nutrients, Phytoplankton, Detritus)
It illustrates a number of interesting features including the coupling of three state variables in a closed cycle, the use of time to control the duration of advection, and the modulus function for cycling annual temperature data over multiple years.
The model state variables are expressed in nitrogen units (mg N m-3), and the calibration is based on:
Baliño, B.M. 1996. Eutrophication of the North Sea, 1980-1990: An evaluation of anthropogenic nutrient inputs using a 2D phytoplankton production model. Dr. scient. thesis, University of Bergen.
Fransz, H.G. & Verhagen, J.H.G. 1985. Modelling Research on the Production Cycle of Phytoplankton in the Southern Bight of the Northn Sea in Relation to Riverborne Nutrient Loads. Netherlands Journal of Sea Research 19 (3/4): 241-250.
This model was first implemented in PowerSim some years ago by one of my M.Sc. students, who then went on to become a Buddhist monk. Although this is a very Zen model, as far as I'm aware, the two facts are unrelated.
Air Pollution Dynamics - Firewood Combustion
The System Dynamics Causal Loop Diagram developed herein shows an initial study of the dynamics among the variables that influences the accumulation of PM in the air, in particular the case of Temuco, in the South of Chile. In Temuco, 97% of the PM inventories comes from the combustion of low quality firewood, which in turns is being burned due to its low price and cultural habits/tradition.
Phyto 1 - PI curve for phytoplankton
The equation is:
Ppot = Pmax I/Iopt exp(1-I/Iopt)
Ppot: Potential production (e.g. d-1, or mg C m-2 d-1)
Pmax: Maximum production (same units as Ppot)
I: Light energy at depth of interest (e.g. uE m-2 s-1)
Iopt: Light energy at which Pmax occurs (same units as I)
The model contains no state variables, just illustrates the rate of production, by making the value of I equal to the timestep (in days). Move the slider to the left for more pronounced photoinhibition, to the right for photosaturation.
2014 Weather & Climate Extreme Loss of Arable Land and Ocean Fertility - The World3+ Model: Forecaster
Environment Demographics Population Growth Population Weather Climate Failure Death Mortality Science Technology Engineering Strategy Economics Politics Fertility Health Services Resources Land Jobs Labor Urban Industrial Rural Lifetime Pollution Regeneration Yield Ocean Sea Fish Plants Animals
Simple phytoplankton and oyster model
Both light and nutrients (e.g. nitrogen) are modelled as forcing functions, and the model is "over-calibrated" for stability.
The phytoplankton model approximately reproduces the spring-summer diatom bloom and the (smaller) late summer dinoflagellate bloom.
Oyster growth is modelled only as a throughput from algae. Further developments would include filtration as a function of oyster biomass, oyster mortality, and other adjustments.
World2 Model of World Dynamics
An element of Perspectives: The Foundation of Understanding and Insights for Effective Action. Register at http://www.systemswiki.org/
Human and Nature Dynamics of Societal Inequality
Eastern Himalayan Mountains
BATHTUB MEAN TIME BETWEEN FAILURE (MTBF) RISK
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 LifeIf 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.
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.
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.
Artic Tundra Food Chain
POPULATION LOGISTIC MAP (WITH FEEDBACK)
the maximum population is set to be one million, and the growth rate constant mu = 3. Nj: is the “number of items” in our current generation.
Delta Nj: is the “change in number of items” as we go from the present generation into the next generation. This is just the number of items born minus the number of items who have died.
mu: is the growth or birth rate parameter, similar to that in the exponential growth and decay model. However, as we extend our model it will no longer be the actual growth rate, but rather just a constant that tends to control the actual growth rate without being directly proportional to it.
F(Nj) = mu(1‐Nj/Nmax): is our model for the effective “growth rate”, a rate that decreases as the number of items approaches the maximum allowed by external factors such as food supply, disease or predation. (You can think of mu as the growth or birth rate in the absence of population pressure from other items.) We write this rate as F(Nj), which is a mathematical way of saying F is affected by the number of items, i.e., “F is a function of Nj”. It combines both growth and all the various environmental constraints on growth into a single function. This is a good approach to modeling; start with something that works (exponential growth) and then modify it incrementally, while still incorporating the working model.
Nj+1 = Nj + Delta Nj : This is a mathematical way to say, “The new number of items equals the old number of items plus the change in number of items”.
Nj/Nmax: is what fraction a population has reached of the maximum "carrying capacity" allowed by the external environment. We use this fraction to change the overall growth rate of the population. In the real world, as well as in our model, it is possible for a population to be greater than the maximum population (which is usually an average of many years), at least for a short period of time. This means that we can expect fluctuations in which Nj/Nmax is greater than 1.
This equation is a form of what is known as the logistic map or equation. It is a map because it "maps'' the population in one year into the population of the next year. It is "logistic'' in the military sense of supplying a population with its needs. It a nonlinear equation because it contains a term proportional to Nj^2 and not just Nj. The logistic map equation is also an example of discrete mathematics. It is discrete because the time variable j assumes just integer values, and consequently the variables Nj+1 and Nj do not change continuously into each other, as would a function N(t). In addition to the variables Nj and j, the equation also contains the two parameters mu, the growth rate, and Nmax, the maximum population. You can think of these as "constants'' whose values are determined from external sources and remain fixed as one year of items gets mapped into the next year. However, as part of viewing the computer as a laboratory in which to experiment, and as part of the scientific process, you should vary the parameters in order to explore how the model reacts to changes in them.
Simple Energy Balance Model
This simulation models the stock and flow of energy between a star, a planet’s surface (primarily its oceans, which are the largest reservoir of heat), and space.The assumptions governing this model are:
1. The planet absorbs a fraction of the shortwave radiation arriving from its star, with that fraction given by (1-A), where A is albedo.
2. The planet radiates longwave infrared radiation into space, with the amount of radiation into space given by σΤe4, where σ is the Stefan-Boltzmann constant and Te is the temperature of the effective radiating level.
3. The atmospheric lapse rate is 6 K/km.
4. If there is an imbalance between shortwave radiation absorbed and longwave radiation emitted, the imbalance affects the temperature of the planet. However, it does not do so instantaneously – the imbalance must heat or cool the mixed layer of the ocean.
5. At the start of the simulation, the planet is extremely close to equilibrium given its default parameters. If any of these parameters are changed, the planet will be out of equilibrium, and will have to adjust.