{ "cells": [ { "cell_type": "markdown", "id": "8c83dd7d", "metadata": {}, "source": [ "## Logistic map and Lyapunov exponent" ] }, { "cell_type": "markdown", "id": "76e77ff7", "metadata": {}, "source": [ "We will plot the bifurcation diagram of a chaotic dynamical system. \n", "We will learn what is Lyapunov exponent and what is chaos. We will understand that certain alhorithms, when using iterations, are extremely sensitive to initial conditions and results might not even be deterministic once chaos appears.\n" ] }, { "cell_type": "markdown", "id": "03101339", "metadata": {}, "source": [ "A chaotic dynamical system is highly sensitive to initial conditions; small perturbations at any given time yield completely different trajectories. The trajectories of a chaotic system tend to have complex and unpredictable behaviors.\n", "\n", "Many real-world phenomena are chaotic, particularly those that involve nonlinear interactions among many agents (complex systems). Examples can be found in meteorology, economics, biology, and other disciplines.\n", "\n", "In this recipe, we will simulate a famous chaotic system: the **logistic map**. This is an archetypal example of how chaos can arise from a very simple nonlinear equation. The logistic map models the evolution of a population, taking into account both reproduction and density-dependent mortality (starvation).\n", "\n", "We will draw the system's bifurcation diagram, which shows the possible long-term behaviors (equilibria, fixed points, periodic orbits, and chaotic trajectories) as a function of the system's parameter. We will also compute an approximation of the system's Lyapunov exponent, characterizing the model's sensitivity to initial conditions.\n", "\n", "\n", "The **logistic map** is defined by the recursive application of the logistic function:\n", "\n", "$$x_{n+1}= r x_n (1-x_n)$$\n", "\n", "It is discrete demographic model, where $x_n$ is a number between zero and one, which represents the ratio of existing population to the maximum possible population.\n", "\n", "The population is expected to increase at a rate proportional to the current population when the population size is small. The proportionality is a parameter $r$. However, when population grows large it starts to overuse available resources, and starvation occurs, hence the growth rate will decrease at a rate proportional to the value obtained by taking the theoretical \"carrying capacity\" of the environment (here 1.0) less the current population.\n", "\n", "\n", "The usual values of interest for the parameter $r$ are those in the interval $[0,4]$, so that $x_n$ remains bounded on $[0,1]$. If $r>4$ the negative population sizes occur. \n", "\n", "Initial condition ($x_0$) is not very important. We will take some small number, like $10^{-5}$. \n", "\n", "Notice that **logistic map** could also be expressed as $f(x) = r x (1-x)$ and we are looking for $f(f(f(...f(x_0)...)))$." ] }, { "cell_type": "markdown", "id": "15f7649e", "metadata": {}, "source": [ "We will also calculate the **Lyapunov exponent**, which characterizes the rate of separation of infinitesimally close trajectories.\n", "\n", "Two trajectories in phase space with initial separation $\\delta Z_0$ \n", "diverge at a rate given by \n", "$$|\\delta Z(t)|\\approx e^{\\lambda t}|\\delta Z_0|.$$ \n", "If $\\lambda>0$, the system is chaotic, because very small change in initial conditions leads to exponentially different solution.\n", "\n", "The formal definition of **Lyapunov exponent** is\n", "$$\\lambda=\\lim_{t\\rightarrow \\infty}\\lim_{|\\delta Z_0|\\rightarrow 0}\\frac{1}{t}\\ln(\\frac{|\\delta Z(t)|}{\\delta Z_0})$$\n", "\n", "For discrete map $x_{n+1}=f(x_n)$\n", "\n", "$$\\delta x_{n+1} \\equiv x^1_{n+1}-x^0_{n+1} = f(x^1_{n})-f(x^0_{n}) \\approx f'(x_{n})\\delta x_n \\approx \\delta x_0 \\prod_{i=0}^n f'(x_i) $$\n", "\n", "After taking the logarithm, and dividing by the number of steps, we get\n", "$$\\lambda = \\lim_{n\\rightarrow\\infty}\\frac{1}{n}\\ln(\\frac{\\delta x_{n}}{\\delta x_0})=\\lim_{n\\rightarrow\\infty}\\frac{1}{n}\\sum_{i=0}^{n-1} \\ln(f'(x_i))$$\n", "\n", "For logistic map, the Lyapunov exponent is hence:\n", "$$\\lambda =\\lim_{n\\rightarrow\\infty}\\frac{1}{n}\\sum_{i=0}^{n-1} \\ln(r (1-2 x_i))$$" ] }, { "cell_type": "markdown", "id": "7cec48fa", "metadata": {}, "source": [ "For the algorithm, we will iterate the logistic function `Nitt` times, and save the last few points (`Nsave`), which will be displayed later.\n", "\n", "The parameter `r` will be discretized with linear mesh of `Npoints` between `ext[0]` and `ext[1]`.\n", "\n", "Because the points corresponding to different `r` require exactly the same number of iterations, and also the same set of operations, it is convenient to do them in parallel. We will thus create an array of points `r[0:Npoints]`, and results will be stored in `data[0:Nsave,0:Npoints]`.\n", "\n", "Here is the code:" ] }, { "cell_type": "code", "execution_count": 30, "id": "630adaa6", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from numba import njit\n", "\n", "@njit \n", "def logistic(r, x):\n", " return r * x * (1 - x)\n", "\n", "@njit\n", "def GiveFewPoints(ext, Npoints, Nitt, Nsave):\n", " # r is array of Npoints, hence we will \n", " # iterate all points simultaneously\n", " r = np.linspace(ext[0],ext[1], Npoints)\n", " # initialize storage for all points we will plot.\n", " data = np.zeros((Nsave,Npoints))\n", " # Lyapunov \n", " lyapunov = np.zeros(Npoints)\n", " x = np.ones(Npoints)*1e-5\n", " for i in range(Nitt):\n", " x = logistic(r, x)\n", " # We compute the partial sum of the\n", " # Lyapunov exponent.\n", " lyapunov += np.log(np.abs(r - 2.0 * r * x))\n", " # We display the bifurcation diagram.\n", " if i >= (Nitt-Nsave):\n", " data[i-(Nitt-Nsave),:]=x\n", " return (r, data, lyapunov/Nitt)" ] }, { "cell_type": "markdown", "id": "4a74d842", "metadata": {}, "source": [ "We call the anove function with `Npoints=1000` and very large number of iterations `Nitt=10000`. We will save the last `Nsave=300` generations. " ] }, { "cell_type": "code", "execution_count": 35, "id": "a5b350d4", "metadata": {}, "outputs": [], "source": [ "ext=np.array([1,4])\n", "(r, data, lyapunov) = GiveFewPoints(ext, 1000, 10000, 300)" ] }, { "cell_type": "markdown", "id": "4778ab34", "metadata": {}, "source": [ "We will plot with two panels. They will share the x-axis, i.e., the same `r` mesh. We will also specify the size of fig.\n", "\n", "The first panel will show logistic map, which are the last 300 points after very large number of iterations. The second is the Lyapunov exponent.\n", "\n", "To select color, we give string `'k'` and comma means plot only dots. We also give them some transparency `alpha=0.25`.\n" ] }, { "cell_type": "code", "execution_count": 34, "id": "85d7edc8", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(8, 9))\n", "\n", "for i in range(np.shape(data)[0]):\n", " ax1.plot(r, data[i,:], 'k,', alpha=0.25)\n", "\n", "ax2.plot(r,lyapunov)\n", "ax2.grid()" ] }, { "cell_type": "markdown", "id": "7e3c50d3", "metadata": {}, "source": [ "Clearly the system is deterministic up to $r=3$, and between $3wikibooks.org" ] }, { "cell_type": "code", "execution_count": null, "id": "73c74e22", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 5 }