Your browser (Internet Explorer 8 or lower) is out of date. It has known security flaws and may not display all features of this and other websites. Learn how to update your browser.

X

Menu

Finance

Clone of POPULATION LOGISTIC MAP (WITH FEEDBACK)

Philipp von Bülow
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.

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

  • 3 months 1 week ago

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

Krupka
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)

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

  • 4 months 1 week ago

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

Nhat_Minh DOAN
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)

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

  • 1 year 1 month ago

Clone of Clone of THE ILLUSION OF A U.S. PUBLIC DEBT MOUNTAIN.

sub cribed
Neoliberalism uses a deceptive narrative to declare that money the government spends into the economy in excesses of the taxes it collects creates a ‘government debt’. In fact, the money the government spends into the economy in excess of the taxes is an income, a benefit for the private sector. When the government issues bonds, the money the private sector uses to buy them via banks comes from a residual cushion of dollars that the government already spent into the economy but has not yet taxed back.  If this were not the case, if the government had taxed back all the money it spent into the economy, then the economy could not function. There would be no dollars in the economy, since the government is the sole supplier of U.S. dollars! In the doted rectangle in the graph you can see that the dollars paid to the government for bonds sits in a dollar asset account. When the government issues bonds it simply provides the public and institutions with a desirable money substitute that pays interest i.e. Treasury bonds. It is a swap of one kind of financial asset for another. To register this swap the government debits the dollar asset account and credits the bond account.  When the time comes to redeem (take back) the bonds, all the government does is revers the swap, and that’s all!  When you look at the total amount of finacial assets in the private sector,  these remain constant at $ 25 BN  after the payment of $ 5 BN taxes. This implies that  no lending of financial assets of the private sector to the government has taken place during the swap operation. The money was always there. The debt mountain is an illusion!

Finance Economy

  • 2 months 1 week ago

Clone of Speculative Feedback Model

Larry Lee
A model of price movements in which the underlying price model behaves as a brownian walk (normally distributed price movements) with speculative feedback using logarithmic discounting of historical prices.

Finance

  • 10 months 3 weeks ago

Pages