Lyapunov exponents of the predator prey model Ljapunovovy ...

436 ImplementationIn this section we explain the algorithms which were used in numerical experimentsand briefly introduce Python 2.7 in which all the numerical experiments were implemented.Python 2.7 is interpreted scripting language which does mean that the source codedoesn’t have to be compiled and it is executed by an interpreter while it is running. Thegreatest advantage of Python 2.7 is that the source codes are short and easy to read. Itis multi-platform and open-source language with many libraries for specific use suchas SciPy and NumPy which are an alternative for some MATLAB functions. For theintroduction to Python 2.7 see [11].Here we give the overlook at libraries used for numerical experiments:• decimal – library used for variable precision arithmetic and work with big numbers• pylab – library for plotting• math – library for basic mathematical operations• numpy – library used for work with matrices, alternative to MATLAB functions• scipy – library for scientific calculations, alternative to MATLAB functions• sympy – library for symbolic calculationsAlgorithms for one-dimensional casesThe following code computes the value of H n,k for the Logistic map directly from definition3.11.1 # import packages2 from decimal import *3 from math import *4 import pylab56 # set the precision7 getcontext() .prec = 40089 # set the initial values10 itermax = 500 # number of iterations11 k = Decimal(300.0) # k12 x = [Decimal(pi) − Decimal(3.0)] # seed 113 xt = [x[0] + Decimal(10 ** (−k))] # seed 21415 # set the initial value of H_1,k16 H = [Decimal(Decimal(log(abs(x[0] − xt[0]),10)) /( Decimal(1.0)) + (k/(Decimal(1.0)))) ]1718 for i in range(itermax):