#### POPULATION LOGISTIC MAP (WITH FEEDBACK)

##### Guy Lakeman

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

- 8 years 1 month ago

#### BATHTUB MEAN TIME BETWEEN FAILURE (MTBF) RISK

##### Guy Lakeman

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.

Environment Economics Finance Mathematics Physics Biology Health Fractals Chaos TURBULENCE Engineering Navier Stokes Science Demographics Population Growth BIFURCATIONS MTBF Risk Failure Strategy

- 5 years 2 months ago

#### FORCED GROWTH INTO TURBULENCE

##### Guy Lakeman

**FORCED GROWTH GROWTH GOES INTO TURBULENT CHAOTIC DESTRUCTION**

**BEWARE pushing increased growth blows the system!**

**(governments are trying to push growth on already unstable systems !)**

The existing global capitalistic growth paradigm is totally flawed

The chaotic turbulence is the result of the concept and flawed strategy 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 limited size working capacity containers (villages communities)

Environment Economics Finance Mathematics Physics Biology Health Fractals Chaos TURBULENCE Engineering Navier Stokes Science Demographics Population Growth BIFURCATIONS MTBF Strategy Weather

- 8 years 1 month ago

#### OVERSHOOT GROWTH INTO TURBULENCE

##### Guy Lakeman

The existing global capitalistic growth paradigm is totally flawed

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 limited size working capacity containers (villages communities)

Environment Economics Finance Mathematics Physics Biology Health Fractals Chaos TURBULENCE Engineering Navier Stokes Science Demographics Population Growth Strategy Weather

- 5 years 2 months ago

#### Totally Accurate Human Population Simulation

##### Mirai

- 3 years 5 months ago

#### Goodwin Model

##### Silvan

**Goodwin Model:**This is a basic version of the Goodwin Model based on Kaoru Yamagushi (2013), Money and Macroeconomic Dynamics, Chapter 4.5 (link)

Equilibrium conditions:

- Labor Supply = 100

- 6 years 4 months ago

#### Clone of Oyster Growth based on Phytoplankton Biomass

##### Andre Freitas

Phytoplankton growth based on on Steele's and Michaelis-Menten equations), where:

Primary Production=(([Pmax]*[I]/[Iopt]*exp(1-[I]/[Iopt])*[S])/([Ks]+[S]))

Pmax: Maximum production (d-1)

I: Light energy at depth of interest (uE m-2 s-1)

Iopt: Light energy at which Pmax occurs (uE m-2 s-1)

S: Nutrient concentration (umol N L-1)

Ks: Half saturation constant for nutrient (umol N L-1).

Further developments:

- Nutrients as state variable in cycle with detritus from phytoplankton and oyster biomass.

- Light limited by the concentration of phytoplankton.

- Temperature effect on phytoplankton and Oyster growth.

Environment Phytoplankton Primary Production Bivalves Growth

- 7 years 8 months ago

#### 3D Printing Projected Growth

##### Jason Blackstone

Inefficiencies in Mass Production support 3D printer growth. Examples of these inefficiencies include: the stockpiling of components and parts, the large amount of working capital required for such stockpiling, profligate waste of materials, and any expenses involved with employing a large number of employees.

Technology for 3D printing will advance through loosely coordinated development in three areas: printers and printing methods, software to design and print, and materials used in printing.

Developed by Jason Blackstone

- 5 years 3 months ago

#### Turkey's population growth and daily water consumption

##### Kadir Özbakır

KADİR ÖZBAKIROZAN AYDIN

- 3 years 2 months ago

#### ST101 Growth with Limits: Basic Model

##### Bob Hawkins

- 8 months 2 weeks ago

#### PannirbrClone4f Eco city micro algae , biogas , bioelectrcidades

##### Pagandai V Pannirselvam

Phytoplankton growth based on on Steele's and Michaelis-Menten equations), where:

Primary Production=(([Pmax]*[I]/[Iopt]*exp(1-[I]/[Iopt])*[S])/([Ks]+[S]))

Pmax: Maximum production (d-1)

I: Light energy at depth of interest (uE m-2 s-1)

Iopt: Light energy at which Pmax occurs (uE m-2 s-1)

S: Nutrient concentration (umol N L-1)

Ks: Half saturation constant for nutrient (umol N L-1).

Further developments:

- Nutrients as state variable in cycle with detritus from phytoplankton and oyster biomass.

- Light limited by the concentration of phytoplankton.

- Temperature effect on phytoplankton and Oyster growth.

Biogas, model as well birefineray option to seperate c02 , chp from bogas model are proposed

Environment Phytoplankton Primary Production Bivalves Growth

- 2 years 6 months ago

#### EasyJet Fliers Model

##### Geoff McDonnell ★

Model of growth from diffusion from John Morecroft's Strategic Modelling and Business Dynamics Book Ch6 p174-191. A discussion of a bigger model of People's Express is in http://bit.ly/HdaGy4 for a related You Tube video by John Morecroft on Reflections on System Dynamics and Strategy

- 8 years 2 months ago

#### Compounding Interest

##### Edythe ★

- 6 years 1 week ago

#### Investment and Output 2

##### Hanns-Jürgen Hodann

- 4 years 6 months ago

#### Star Framework

##### biren pat

- 8 years 4 months ago

#### Invasive Species 2

##### Rick Brown

- 2 years 6 months ago

#### model

##### vinay

model

- 8 years 4 months ago

#### Oyster Growth based on Phytoplankton Biomass

##### João Lopes

Phytoplankton growth based on on Steele's and Michaelis-Menten equations), where:

Primary Production=(([Pmax]*[I]/[Iopt]*exp(1-[I]/[Iopt])*[S])/([Ks]+[S]))

Pmax: Maximum production (d-1)

I: Light energy at depth of interest (uE m-2 s-1)

Iopt: Light energy at which Pmax occurs (uE m-2 s-1)

S: Nutrient concentration (umol N L-1)

Ks: Half saturation constant for nutrient (umol N L-1).

Further developments:

- Nutrients as state variable in cycle with detritus from phytoplankton and oyster biomass.

- Light limited by the concentration of phytoplankton.

- Temperature effect on phytoplankton and Oyster growth.

Environment Phytoplankton Primary Production Bivalves Growth

- 7 years 9 months ago

#### Simple Market Saturation

##### Robert Koshinskie

- 12 months 1 day ago

#### Miniwelt nach Bossel

##### Thomas Neher

- 4 years 5 months ago

#### Learning and Learn Level

##### Jo Fisch

Holistic Learning Living Loving Life-work Growth Entrepreneurship Management

- 5 years 7 months ago

#### Advanced Community Growth Model

##### Werner Schoenfeldinger ★

- 8 years 1 month ago

#### Simpel Population Model

##### PORTSCHELLER

- 6 years 3 weeks ago

#### Population of France (Developed) Over Time

##### Christopher Hartline

- 5 years 3 weeks ago