ME5010 Project

Math Project

Logistic Map

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

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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.

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2. 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)

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3. 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)

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4. spr_traingle.py.py Generate sierpinski traingle.

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5. bansli_ferm.py
   Generation of Barnsley Fern.

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6. cobweb_r_changing.m
   Animated cobweb graph for logistic map

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

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8. generalizedVerhulst.m
   Generalized logistic equation

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Contributors :

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