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ME5010 Project

Math Project

Logistic Map

$\mathbf{x_{n+1} = rx_n(1-x_n)}$


Language

  • Python10.+ Libraries used :
    • numpy : pip install numpy (Handling arrays)
    • matplotlin : pip install matplotlib (Plotting)
    • numba : pip install numba(Speed optimizer)
  • Matlab

Code File Description

  1. logistic_interactive.py

See how logistic equation progression varies, I have coded two sliders to adjust r and x. You can even zoom in the bifurcation map, It's really helpful in tallying what's happening to map with as r varies.


  1. lprandom.py Used to generate random number at constant r = 4, here seed is x. This file have two functions.
  • lprandom_real(n,seed = None) :
    • n is number of random numbers you want to generate,
    • seed(optional parameter) is initial value of x, If it's not specified program use epoch time to generate it
    • It returns uniformly distributed array of numbers generated via logistic equation and a seed. (array,seed) Sample use case :
import numpy as np
import lprandom.py as lp
random_number_array,seed = lp.lprandom_real(10000)
  • lprandom_real_un(n,seed = None) :
    • n is number of random numbers you want to generate,
    • seed(optional parameter) is initial value of x, If it's not specified program use epoch time to generate it
    • It returns array of numbers generated via logistic equation and a seed . (array,seed) Sample use case :
import numpy as np
import lprandom.py as lp
random_number_array,seed = lp.lprandom_real_un(10000)

  1. pseudo_random_gen.py Used to generate random number at constant . This file have one functions. Changes seed after every number generation , (x,r,N) all three parameters are seeds.
  • get_pnr(n) :
    • n is number of random numbers you want to generate,
    • It returns array of numbers generated via logistic equation Sample use case :
import numpy as np
import pseudo_random_gen.py as pn
random_number_array = pn.get_pnr(10000)

  1. spr_traingle.py.py Generate sierpinski traingle.


  1. bansli_ferm.py
    Generation of Barnsley Fern.


  1. cobweb_r_changing.m
    Animated cobweb graph for logistic map


  1. logistic.m
    Logistic map to model a business model


  1. generalizedVerhulst.m
    Generalized logistic equation


Contributors :

  • TS Rudramani
  • Nitesh Singh
  • Shyam Sridhar
  • Pawan Kumar
  • notcamecase01 (Aman)

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