yuanx749/complex_systems

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demo/demo.ipynb

Summary

Maintainability
Test Coverage
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Demo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "remove_cell"
    ]
   },
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import sys\n",
    "from pathlib import Path\n",
    "\n",
    "ROOT = Path.cwd().parent\n",
    "sys.path.insert(0, str(ROOT))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import matplotlib_inline.backend_inline\n",
    "matplotlib_inline.backend_inline.set_matplotlib_formats(\"png\")\n",
    "\n",
    "from mcs import DE, ODE, CA, PDE, Net"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lotka-Volterra equations\n",
    "$dx/dt = ax - bxy$  \n",
    "$dy/dt = dxy - cy$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ode = ODE(max_step=10000, dim=2, dt=0.01)\n",
    "ode.initialize(x0=[10, 10])\n",
    "ode.simulate(f=ode.lv(a=1.1, b=0.4, c=0.4, d=0.1))\n",
    "fig = ode.visualize()\n",
    "ax = fig.axes[0]\n",
    "ax.set_xlabel('time')\n",
    "ax.set_ylabel('states')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Game of life"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9Cfj3Yv1fA88CF4H/Aj4w7VrH6v4kcGoItZbdfAadWRIeoDNLwmE3S8JhN0vCYTdLwmE3S8JhN0vCYTdLwmE3S+L/AXMt2MrftyEbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ca = CA(max_step=100, size_x=50, size_y=50)\n",
    "ca.initialize()\n",
    "ca.simulate(F=ca.game_of_life)\n",
    "fig = ca.visualize()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Turing pattern\n",
    "Reaction-diffusion equations:\n",
    "\n",
    "$\\partial u/\\partial t = a(u-h) + b(v-k) + D_u \\Delta u$  \n",
    "$\\partial v/\\partial t = c(u-h) + d(v-k) + D_v \\Delta v$\n",
    "\n",
    "Initial small pertubations are applied to the homogeneous equilibrium state $(h, k)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pde = PDE(max_step=2500, dim=2, dt=0.02, dh=0.01, size=100)\n",
    "pde.initialize()\n",
    "pde.simulate(F=pde.turing(a=1.0, b=-1.0, c=2.0, d=-1.5, h=1.0, k=1.0, Du=0.0001, Dv=0.0006, dh=0.01))\n",
    "figs = pde.visualize(indices=[0])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Synchronization of network of coupled oscillators\n",
    "$d\\theta_i/dt = b\\theta_i + a\\sum_{j\\in N_i}(\\theta_j-\\theta_i)$\n",
    "\n",
    "Stable trajetory: $b - a\\lambda_2 < 0$, where $a\\ge 0$ and $\\lambda_2$ is the second smallest eigenvalue of Laplacian matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "net = Net(max_step=2000)\n",
    "net.initialize()\n",
    "net.simulate(a=2, b=0.9, dt=0.01)\n",
    "fig = net.visualize(step=0)\n",
    "fig = net.visualize()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Tags",
  "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": "3.8.10"
  },
  "vscode": {
   "interpreter": {
    "hash": "0f006c2f46c8cc278cf6031d97486ee4b9471c9960d63808982c622a12df145a"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}