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Clone of The Logistic Map

Nicole M Radziwill

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 written


 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.
To 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

Environment Economics Fractals Chaos Mathematics Population

  • 4 years 11 months ago

Population of France (Developed) Over Time (with Uncertainty)

Christopher Hartline
Here we model the population of France given data between 1960 and 2013 from We used the crude birth rate and crude death rate for every 5 years since 1960 to 2005, and the rates every year from 2005 to 2013. To forecast, we used the slope of the net birth rate to calculate when the net birth rate would be zero, and used this year for our birth and death rates to are equal to zero.  We assumed no net movement of people into or out of France. We add that at any given time, our knowledge of the birth and death rates is not accurate, where our rates vary with a standard deviation equal to the standard deviation in the rates from 1960 to 2013

Population Growth

  • 4 years 11 months ago

Ireland Population

Novelyn Verran
Birth Rate​
Death Rate

Immigration Rate

Emigration Rate

Biology Population

  • 3 years 2 months ago


Tsogbadrakh Banzragch
Population is matrix vector:​{Females: {Age1: 5, Age2: 6, Age3: 5, Age4: 3, AgeMore: 1}, Males: {Age1: 4, Age2: 4, Age3: 4, Age4: 1, AgeMore: 0}}
Birth rate is
{Females: {Age1: .49, Age2: 0, Age3: 0, Age4: 0, AgeMore: 0}, Males: {Age1: .51, Age2: 0, Age3: 0, Age4: 0, AgeMore: 0}}

Childbearing Age is {Females: {Age2, Age3, Age4}}
Births Flow is[Birth rate]*sum([Population Rabbits].Females.Age2,[Population Rabbits].Females.Age3,[Population Rabbits].Females.Age4)


  • 3 years 2 months ago

Estado psicológico de uma população (MBA)

João Paulo Scoralick
Modelagem do estado psicológico de uma população. Inicialmente, todos os indivíduos estão no estado "Calmo". Com o passar do tempo e com as interações mútuas, há o surgimento e progressivo aumento do total de indivíduos com raiva (estado "Raivoso"). Deste estado e, com o passar do tempo, os indivíduos podem evoluir mentalmente e atingirem o estado "Indiferente", nos quais eles se tornam indiferentes à qualquer interação. Outra possibilidade é o indivíduo se enriquecer e, assim, atingir a felicidade (estado "Feliz").

Population Psychological States Of Mind Interactions

  • 4 years 6 months ago