Task on Logistic Map and World GDP Data Analysis

Review the main properties of the discrete time dynamics defined by the logistic map equation

Read the first Lecture handouts please.

1) Download the classical introductory paper and read it

http://abel.harvard.edu/archive/118r_spring_05/docs/may.pdf
Read an article in Wikipedia

https://en.wikipedia.org/wiki/Logistic_map

Review the main properties of the discrete time dynamics defined by this equation very briefly in the report (2-3 pages, not more; try to avoid copy-past, use your own words). (10 marks from 100)

1) Take K=1. Starting from the initial point P0=0.5 compute and plot the dynamics Pn for 50 time steps and r=0.6, 1.7, 2.8, 3.2, 3.6, 3.9
Try additionally two initial points: P0=0.2 and P0=0.8.

What do you observe?

Describe the difference from the continuous logistic equation.

Write a brief report. (10 marks from 100)

2) Take GDP data for the whole world from 1961 to 2018 (from the World Bank

site http://data.worldbank.org/indicator/NY.GDP.MKTP.CD ).

Read the Excel file, extract data for the whole world, plot data by yourself (MatLab is preferable). Describe the dynamics qualitatively: intervals of growth, failures, deep crises, etc. Report. 

Prepare a scatter plot from pairs

Comment briefly, is there a functional dependence between

(as you can see from this plot).

Use Fraction of Variance Unexplained for evaluation of this accuracy. What are evaluated r and K?

Split the time period 1960-2016 into 6 approximately equal windows. Repeat calculations inside each time window. Plot r, K, and regression error as functions of time interval (6 values of each time interval and the values for the whole interval [1960,2018]). Represent the results in a table and graphically.

What do you see? Report. (20 marks from 100) 

3) Select two countries for analysis. Take GDP data for your selected countries from the World Bank site (from 1961 to 2016). Pairs of selected countries should be different for different students!

http://data.worldbank.org/indicator/NY.GDP.MKTP.CD

Repeat the analysis from task 2 for two selected countries. Report (30 marks from 100)

4) For three time series (world GDP and two countries GDPs) simulate the GDP with the empirical initial conditions using logistic map and the evaluated
coefficients.

You have two evaluations of r and K: the global estimate for the whole period, and estimate in windows, as functions of time. Therefore, you have two
models for each time series. Find predictions for both.

Compare the computed time series to original data plots. Is it fine? How do you evaluate accuracy of these models? (30 marks from 100)

Read the first Lecture handouts please.

1) Download the classical introductory paper and read it

http://abel.harvard.edu/archive/118r_spring_05/docs/may.pdf
Read an article in Wikipedia

https://en.wikipedia.org/wiki/Logistic_map

Review the main properties of the discrete time dynamics defined by this equation very briefly in the report (2-3 pages, not more; try to avoid copy-past, use your own words). (10 marks from 100)

1) Take K=1. Starting from the initial point P0=0.5 compute and plot the dynamics