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Population calculation using command and control in cycles

In this example, the calculation of population dynamics is realised on the basis of a non-linear, discrete model.

In the model, the population in a given year p(n) is proportional to the population of the previous year, p(n - 1), multiplied by the reproduction rate, p. However, resources are limited by L people, thus creating a negative impact on the population.

The figure below shows the model itself.

image.png

Next, let's connect the auxiliary function to start the model and declare initial states for it.

In [ ]: 
function run_model( name_model)
    
    Path = (@__DIR__) * "/" * name_model * ".engee"
    
    if name_model in [m.name for m in engee.get_all_models()] # Проверка условия загрузки модели в ядро
        model = engee.open( name_model ) # Открыть модель
        model_output = engee.run( model, verbose=true ); # Запустить модель
    else
        model = engee.load( Path, force=true ) # Загрузить модель
        model_output = engee.run( model, verbose=true ); # Запустить модель
        engee.close( name_model, force=true ); # Закрыть модель
    end
    sleep(5)
    return model_output
end
Out[0]:
run_model (generic function with 1 method)

Let's set the starting conditions as follows:

L = 1.0e6

p(0) = 1.0e5

r, we will change in the course of modelling:

  1. 1.5e-6 (the system converges)
  2. 2,2e-6 (2-cycle system)
  3. 2.5e-6 (4-cycle system)
  4. 2.56e-6 (8-cycle system)
In [ ]: 
L = 1.0e6;
p0 = 1.0e5;
r_arr = [1.5e-6,2.2e-6,2.5e-6,2.56e-6];

Let's run the model in a cycle changing the value of r.

In [ ]: 
Population = zeros(21,4)
r = 0;
for i in 1:4  
    r = r_arr[i]
    run_model("population") # Запуск модели.
    P = collect(simout["population/Rounding Function.1"]);
    Population[:,i] = P.value
end 

Building...
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Building...
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Building...
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Building...
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Let's display and compare the obtained results.

In [ ]: 
plot(Population, label=["r = 1.5e-6" "r = 2.2e-6" "r = 2.5e-6" "r = 2.56e-6"])
Out[0]:

Conclusion

According to the results of the model, we see that the ideal population size is 1 million people, and with the coefficient 1.5e-6. In other cases, we observe population growth followed by population decline. In the case of scarcity of resources and the larger the coefficient r, the greater the diversity in population growth.

Blocks used in example