#### Clone of POPULATION LOGISTIC MAP (WITH FEEDBACK)

##### Roman Knaus

The simulation integrates or sums (INTEG) the Nj population, with a change of Delta N in each generation, starting with an initial value of 5.The equation for DeltaN is a version of Nj+1 = Nj + mu (1- Nj / Nmax ) Nj

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.

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.

Environment MATHS Mathematics Chaos Fractals BIFURCATION Model Economics Finance TURBULENCE Population Growth DECAY STABILITY SUSTAINABLE Engineering Science Demographics Strategy

- 3 years 9 months ago

#### Causal loop diagram of savings account - simple interest

##### Henny van Dongen ★

- 6 months 1 day ago

#### Investimento Mensal

##### Kaike Alves

- 5 months 2 weeks ago

#### Clone of Housing Demand and Unemployment

##### Ricky Su

- 5 years 9 months ago

#### Clone of Oil Price Influencers (3-Loop)

##### R Link

Causal loop diagram illustrating a variety of feedback loops influencing the price of oil.

- 5 years 1 month ago

#### Clone of ISD Savings Plan

##### Kevin Collins

- 4 years 3 months ago

#### Clone of Factoring platform on blockchain with loop

##### Olga Konoval

We are modeling future cash flows in the system consisting of three interacting parties, one of which secures deals between the two others which do not trust each other.

- 3 years 10 months ago

#### Clone of THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES CHAOTIC TURBULENCE (+controls)

##### Ricardo Santana Cabello

THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION

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)

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)

Environment Economics Finance Mathematics Physics Biology Health Fractals Chaos TURBULENCE Engineering Navier Stokes Supply Demand Strategy

- 3 years 4 months ago

#### Fixed rate mortgage deal model

##### Mark de Cates

Models the repayment of a mortgage, with a fixed-term fixed-rate deal.

e.g. for an up-front £1495 fee, you get a fixed interest rate of 1.22% for 2 years, followed by variable rate).

After the deal ends, the 'variable' rate is currently constant, but could be set via a converter instead to model different predictions of future interest rates.

e.g. for an up-front £1495 fee, you get a fixed interest rate of 1.22% for 2 years, followed by variable rate).

After the deal ends, the 'variable' rate is currently constant, but could be set via a converter instead to model different predictions of future interest rates.

- 1 year 1 month ago

#### Stock-Flow diagram of savings account - compound interest

##### Henny van Dongen ★

Extremely basic stock-flow diagram of compound interest with table and graph output in interest and savings development per year. Initial deposit, interest rate, yearly deposit and withdrawal can all be modified in Dutch.

- 5 months 4 weeks ago

#### Clone of HODL vs. cloud mining

##### Joffrey

Simulation compares Bitcoin cloud mining opportunity (hashflare.io) to HODL.The model does not calculate with mining difficulty, pool's efficiency and changes in fees. Using monthly cloud fees as of the end of November 2017.Used https://www.coinwarz.com/calculators/bitcoin-mining-calculator for mining calculations.

- 2 years 2 weeks ago

#### Clone of Clone of ABM-CRA

##### Domenico Suppa

- 6 years 12 months ago

#### EMMER GRILLL

##### Julia Franken

Finance

- 2 years 10 months ago

#### EMMER BOIIIII

##### Julia Franken

Finance

- 2 years 10 months ago

#### Eric Tymoigne Monetary Sovereignty

##### Geoff McDonnell ★

WIP Summary of 2020 article Monetary Sovereignty: Nature, Implementation, and Implications by Eric Tymoigne

- 12 months 4 days ago

#### Clone of Negative Interest

##### Brian Dowling

Demonstrate that the same diagram is appropriate whether the interest rate is positive or negative.

- 2 years 5 months ago

#### Clone of Einfuehrung_neues_Athentisierungsverfahren_fuer_Kunden

##### mephew

- 6 years 9 months ago

#### Clone of Vermögensentwicklung nominal und real

##### Holger Arndt

Das Modell sensibilisiert für die langfristigen Folgen von Inflation und Besteuerung bei Kapitalanlagen

- 6 years 3 months ago

#### Clone of Allowance or Money Earned

##### emad

Php1500 all in all the cost

Php2000 the desired or needed money to be able to save

Php500 to Php1000 are usually given

Php2000 the desired or needed money to be able to save

Php500 to Php1000 are usually given

- 8 years 6 months ago

#### Clone of Clone of Einfuehrung_neues_Athentisierungsverfahren_fuer_Kunden

##### mephew

- 6 years 9 months ago

#### Clone of factoring platform on blockchain

##### Aby Mammen Mathew

We are modeling future cash flows in the system consisting of three interacting parties, one of which secures deals between the two others which do not trust each other.

- 3 years 5 months ago

#### Clone of Test - Bank Interest

##### Bibhushit Chaudhary

- 4 years 6 months ago

#### Clone of Bob - Expanded

##### Chris Magnuson

This is what I would imagine how most of the US's personal finances look: The individual has a retirement account set up or will be getting pensions upon retiring and has replaced his or her rent payment with a mortgage, which will go away after 15-30 years.

- 5 years 3 months ago

#### mutual funds savings value overtime (IDR)

##### Nurul Khairiza Utami

the simulation shows how our money grows overtime as we keep investing our money every month in money market mutual funds. But overtime monetary value keeps growing up with constant rate of 3%, so what this simulation shows us is the real value of the money we invest in mutual funds that have a certain rate of interest.

- 8 months 1 week ago