{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerical exercises" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- visualisation of phase portraits" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# importing the needed python libraries\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from typing import Tuple\n", "from scipy.integrate import solve_ivp # used in numerical integration" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Example 2.8.1 in Strogatz\n", "Solve system $\\dot{x} = x(1-x)$ numerically." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the slope field in (t, x) plane." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Quiver" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Quiver is a function in matplotlib. See the documentation [here](https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.quiver.html).\n", "* The function can be used to plot a field with arrows pointing from (t,x) to (t+u, x+v) at each point of a defined grid. We get arrows with slope dx/dt by setting u=1 and v=dx/dt at each point." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# creating grid points\n", "t, x = np.meshgrid(np.arange(0,4, 0.25), np.arange(0,2, 0.15))\n", "\n", "# v=dx/dt and u=1 at each point\n", "V = x*(1-x)\n", "U = np.ones(V.shape)\n", "\n", "# setting up the plot and labels\n", "fig, ax = plt.subplots()\n", "ax.set_title('Slope field')\n", "ax.set_xlabel('t')\n", "ax.set_ylabel('x')\n", "\n", "# plots arrows pointing from (t,x) to (t+u, x+v) at each point of the grid\n", "q = ax.quiver(t, x, U, V, angles='xy')\n", "\n", "# quiverkey function is for labelling the arrows - position (X, Y) and length U \n", "ax.quiverkey(q, X=0.8, Y=1.045, U=2,\n", " label='dx/dt', labelpos='E')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Streamplot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Streamplot is also a function in matplotlib, see the documentation [here](https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.streamplot.html?highlight=streamplot#matplotlib.pyplot.streamplot)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X, T = np.mgrid[0:2:100j, 0:10:100j]\n", "V = X*(1-X)\n", "U = np.ones(V.shape)\n", "\n", "fig, ax = plt.subplots()\n", "ax.set_title('Stream plot with color corresponding to speed')\n", "ax.set_xlabel('t')\n", "ax.set_ylabel('x')\n", "\n", "# plotting the speed (dx/dt) as the color\n", "# using the absolute value of V because the arrows are already indicating the direction\n", "plt.streamplot(T, X, U, V, color=np.abs(V), linewidth=2, cmap=plt.cm.autumn)\n", "plt.colorbar()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X, T = np.mgrid[0:2:100j, 0:10:100j]\n", "V = X*(1-X)\n", "U = np.ones(V.shape)\n", "\n", "fig, ax = plt.subplots()\n", "ax.set_title('Stream plot with linewidth corresponding to speed')\n", "ax.set_xlabel('t')\n", "ax.set_ylabel('x')\n", "\n", "speed = np.abs(V)\n", "lw = 5*speed/speed.max() # scaling to convenient range\n", "\n", "# plotting the speed (dx/dt) as the linewidth\n", "plt.streamplot(T, X, U, V, density=0.6, color='k', linewidth=lw)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Numerical integration and plotting trajectories" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* solve_ivp is a function in scipy. Documentation [here](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html?highlight=solve_ivp#scipy.integrate.solve_ivp)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# defining a function to simulate the differential equation\n", "def simulate(n_timesteps: int, state0: list=[1.0], h: float=0.01) -> Tuple[np.ndarray, np.ndarray]:\n", "\n", " def diff(t, state):\n", " x = state \n", " return x * (1 - x)\n", "\n", " t = np.arange(0, n_timesteps * h, h)\n", " \n", " sol = solve_ivp(diff, \n", " y0=state0,\n", " method='RK45',\n", " t_span=(0.0, n_timesteps*h),\n", " dense_output=True)\n", " \n", " return sol.sol(t).T, t" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# integration timestep\n", "timestep = 0.1\n", "\n", "# creating two trajectories, starting states x0: 0.2 and 13\n", "data, data_t = simulate(100, state0 = [0.2, 1, 13], h = timestep)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t, x = np.meshgrid(np.arange(0,10, 0.5), np.arange(0,2.1, 0.1))\n", "V = x*(1-x)\n", "U = np.ones(V.shape)\n", "\n", "# plotting the slope field\n", "fig, ax = plt.subplots()\n", "q = ax.quiver(t, x, U, V, angles='xy')\n", "ax.quiverkey(q, X=0.8, Y=1.03, U=2,\n", " label='dx/dt', labelpos='E')\n", "\n", "# plotting the simulated trajectories\n", "plt.plot(data_t, data)\n", "\n", "ax.set_ylim(0, 2)\n", "ax.set_title('Slope field')\n", "ax.set_xlabel('t')\n", "ax.set_ylabel('x')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that if one trajectory dx/dt should diverge, i.e., obtain huge values, say, beyond a value $t = t_d$, then integration will stop at $t = t_d$ for all trajectories. If you want to extend integration beyond $t = t_d$ for other trajectories, you must do the integration for that trajectory separately. Separate integration in the previous example:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# integration timestep\n", "timestep = 0.1\n", "\n", "# creating two trajectories, starting states x0: 0.2 and 13\n", "data, data_t = simulate(100, state0 = [0.2], h = timestep)\n", "data2, data_t2 = simulate(100, state0 = [1], h = timestep)\n", "data3, data_t3 = simulate(100, state0 = [13], h = timestep)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t, x = np.meshgrid(np.arange(0,10, 0.5), np.arange(0,2.1, 0.1))\n", "V = x*(1-x)\n", "U = np.ones(V.shape)\n", "\n", "# plotting the slope field\n", "fig, ax = plt.subplots()\n", "q = ax.quiver(t, x, U, V, angles='xy')\n", "ax.quiverkey(q, X=0.8, Y=1.03, U=2,\n", " label='dx/dt', labelpos='E')\n", "\n", "# plotting the simulated trajectories\n", "plt.plot(data_t, data)\n", "plt.plot(data_t2, data2)\n", "plt.plot(data_t3, data3)\n", "\n", "ax.set_ylim(0, 2)\n", "ax.set_title('Slope field')\n", "ax.set_xlabel('t')\n", "ax.set_ylabel('x')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Note that three intial values $x(t=0)$ were needed to plot all the qualitatively different $x(t)$: $x(0) < x^*$, $x(0) = x^*$, and $x(0) > x^*$, where $x^*$ is the fixed point value." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## More plotting examples\n", "See examples in the documentation [here](https://matplotlib.org/3.1.1/gallery/images_contours_and_fields/quiver_simple_demo.html#sphx-glr-gallery-images-contours-and-fields-quiver-simple-demo-py) and [here](https://matplotlib.org/3.1.1/gallery/images_contours_and_fields/quiver_demo.html#sphx-glr-gallery-images-contours-and-fields-quiver-demo-py) for quiver and [here](https://matplotlib.org/3.1.1/gallery/images_contours_and_fields/plot_streamplot.html) for streamplot. " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 4 }