Stack Overflow
Stack Overflow

Questions tagged [lorenz-system]

The Lorenz system is a system of ordinary differential equations (the Lorenz equations, note it is not Lorentz) first studied by Edward Lorenz.

The Lorenz system is a system of ordinary differential equations (the Lorenz equations, note it is not Lorentz) first studied by Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure eight.

References:

17 questions
3
votes
1 answer

Python Nolds: how to get proper value for Lorenz system

currently i use following code to generate lorenz series def generate(x, stop=10000, s=10, b=8/3, r=28): def lor(v): return np.array([s * (v[1] - v[0]), v[0] * (r - v[2]) - v[1], v[0] * v[1] - b * v[2]]) ret = [] step = 0.1 …
melancholique melancholique
  • 31
  • 3
2
votes
1 answer

How to solve Lorenz 96 model using Runge–Kutta method?

I have written the below code to solve Lorenz 96 model using Runge–Kutta method, but the results are not reliable as can be seen in the below figure: The correct relationship between three variables is as follows: How can I modify the code to…
hamid mohebzadeh
  • 127
  • 5
2
votes
1 answer

RuntimeWarning with The Lorenz Equations

I am trying to do Lorenz's equations in python (I am following exercise 8.3 from Mark Newman - Computational Physics (2012, CreateSpace Independent Publishing Platform)) I already got the graphics and everything looks "correct". This is probably a…
Miguel Godinho
  • 125
  • 8
2
votes
1 answer

Gnuplot - Plot graph with continuously varying line color - plot with color fade / transition

I am using GNU plot (gnuplot) to plot some output data from integration of a strange attractor (see Wikipedia) - and as this is a strange attractor the line "rolls around itself in 3D space". This makes it difficult to see what happens when plotting…
FreelanceConsultant
  • 13,167
  • 27
  • 115
  • 225
1
vote
0 answers

Solve and plot Lorenz equations for two different initial conditions and two values of rho in julia

My goal is to solve lorenz equations and plot them as it shows in the figure. I have two different initial conditions [x0, 1, 0] and x0= 0 then x0 =1* 10^-5 the two values of rho are ρ= 14 and ρ=28. I wrote this code in julia but I'm getting errors…
Hana Bachi
  • 11
  • 3
1
vote
1 answer

In Python: How to make a bifurcation diagram of the Lorenz system under a varying parameter value?

So, I've seen the coded solution to my question in Mathematica, but with very little understanding of mathematica, I havn't been able to reproduce it yet. This is what I'm trying to do with Python:…
Cobra
  • 13
  • 5
1
vote
3 answers

Lorenz attractor with Runge-Kutta python

Hello I have to program a python function to solve Lorenz differential equations using Runge-Kutta 2cond grade sigma=10, r=28 and b=8/3 with initial conditions (x,y,z)=(0,1,0) this is the code i wrote, but it throws me an error saying overflow…
Juan De Dios Rojas
  • 25
  • 1
  • 5
1
vote
3 answers

Runge Kutta constants diverging for Lorenz system?

I'm trying to solve the Lorenz system using the 4th order Runge Kutta method, where dx/dt=a*(y-x) dy/dt=x(b-z)-y dx/dt=x*y-c*z Since this system doesn't depend explicity on time, it's possibly to ignore that part in the iteration, so I just…
Matías Saavedra
  • 13
  • 3
1
vote
1 answer

Lorenz System in MATLAB- making of simulation and movie

I am trying to simulate trajectories in the Lorenz System in MATLAB, with currently using the following code - clear all clf; clc; % Solution [t1,x1] = ode45('g',[0 30],[0;2;0]); [t2,x2] = ode45('g2',[0 30],[0;2.001;0]); [C,h] = size(x2); ang =…
tobias mulder
  • 13
  • 2
0
votes
0 answers

Which "real-world" tasks can be solved with using Lorenz Attractor?

I created a notebook with analysis of Lorenz Attractor and now I'm looking for practical tasks which can be solved with it. The reason why I need this is because without any practical tasks my notebook doesn't bring anything innovative and isn't…
rastr__
  • 23
  • 4
0
votes
0 answers

phase plane analysis of lorenz equations

Im trying to plot the phase plane analysis of lorenz equations. For example the saddle,spiral,nodes. This is my code x = np.linspace(-40,40,100) y = np.linspace(-60,50,100) z = np.linspace(-100,100,100) rho=28 beta=8/3 sigma=10 xx,yy =…
Claudia Yeboah
  • 1
0
votes
1 answer

Lorenz Attractor

I have a question related to numpy's empty() function. I am trying to plot a chaos graph, in the meanwhile, I have been using np.empty() function to create empty arrays consisting of 20,000 elements. The code works perfectly fine when I use the…
Trissa Shamp
  • 19
  • 6
0
votes
1 answer

How to stack filled areas instead of overlapping them using ggplot?

I have a Lorenz Curve graph that I filled by factor variables (male and female). This was done simply enough and overlapping was not an issue because there were only two factors. Wage %>% ggplot(aes(x = salary, fill = gender)) + stat_lorenz(geom…
Emir Dakin
  • 148
  • 5
0
votes
1 answer

Using different time point sets (parameter t) for python scipy builtin function ODEINT

I am working on the Lorenz system. I used the 'scipy.integrate.odeint' builtin function to integrate as suggested on Wikipedia1. Lorenz system has three variables: x, y, z. When I compared the evolution of x for two Lorenz systems with same initial…
Abhilash CH
  • 3
  • 2
0
votes
1 answer

What is the most descriptive way to plot Lorenz System?

I am (numerically) solving the Lorenz System by using different methods. I am plotting it using matplotlib but I would like a way to distinguish better the points. For example: Let's assume the points to be plotted are stored in the array a which…
D1X
  • 5,025
  • 5
  • 21
  • 36
1
2