francescoAndLauraInteractive.ipynb

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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import odeint\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import GridBox, Layout, interactive_output\n",
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def love_dynamics(y, t, params):\n",
    "    \"\"\"differential equation model\n",
    "\n",
    "    Args:\n",
    "        y (array): arrya of initial conditions\n",
    "        t (array): time intervals\n",
    "        p (array): parameters to use\n",
    "\n",
    "    Returns:\n",
    "        array: array of differential equation results\n",
    "    \"\"\"\n",
    "    alpha1, alpha2, beta1, beta2, gamma1, gamma2, A1, A2, x_star2, epsilon, mu, delta = params\n",
    "    x1, x2, z2 = y\n",
    "\n",
    "    RL1 = beta1 * x2 * (1 - (x2 / x_star2)**2)\n",
    "    RL2 = beta2 * x1 + gamma2 * A1 / (1 + delta * z2)\n",
    "    dz2dt = epsilon * (mu * x2 - z2)\n",
    "\n",
    "    dx1dt = -alpha1 * x1 + RL1 + gamma1 * A2\n",
    "    dx2dt = -alpha2 * x2 + RL2\n",
    "\n",
    "    return [dx1dt, dx2dt, dz2dt]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_conditions = [0, 0, 0]\n",
    "t = np.linspace(0, 20, 1000)  # Set time period to 20\n",
    "\n",
    "slider_style = {'description_width': 'initial'} \n",
    "slider_layout = Layout(width='auto')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_plot(alpha1, alpha2, beta1, beta2, gamma1, gamma2, A1, A2, x_star2, epsilon, mu, delta):\n",
    "    params = [alpha1, alpha2, beta1, beta2, gamma1, gamma2, A1, A2, x_star2, epsilon, mu, delta]\n",
    "    solution = odeint(love_dynamics, initial_conditions, t, args=(params,))\n",
    "    \n",
    "    plt.figure(figsize=(16, 5))\n",
    "\n",
    "    # Time series\n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.plot(t, solution[:, 0], label='Laura', color='tab:blue')\n",
    "    plt.plot(t, solution[:, 1], label='Francesco', color='tab:pink')\n",
    "    plt.xlabel('Time')\n",
    "    plt.ylabel('Feelings')\n",
    "    plt.title('Dynamics of Romantic Relationship')\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "\n",
    "    # Phase diagram\n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.plot(solution[:, 0], solution[:, 1])\n",
    "    plt.xlabel('x1')\n",
    "    plt.ylabel('x2')\n",
    "    plt.title('Phase Diagram')\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "# Parameters\n",
    "alpha1_slider = widgets.FloatSlider(value=3.6, min=-10, max=10, step=0.01, description='Forgetting Coef. Romeo (alpha1)', style=slider_style, layout=slider_layout)\n",
    "alpha2_slider = widgets.FloatSlider(value=1.2, min=0, max=10, step=0.01, description='Forgetting Coef. Juliet (alpha2)', style=slider_style, layout=slider_layout)\n",
    "beta1_slider = widgets.FloatSlider(value=1.2, min=0, max=10, step=0.01, description='Reactiveness to Love Juliet on Romeo (beta1)', style=slider_style, layout=slider_layout)\n",
    "beta2_slider = widgets.FloatSlider(value=6, min=0, max=10, step=0.01, description='Reactiveness to Love Romeo on Juliet (beta2)', style=slider_style, layout=slider_layout)\n",
    "gamma1_slider = widgets.FloatSlider(value=1.2, min=0, max=10, step=0.01, description='Reactiveness to Appeal Juliet on Romeo (gamma1)', style=slider_style, layout=slider_layout)\n",
    "gamma2_slider = widgets.FloatSlider(value=6, min=0, max=10, step=0.01, description='Reactiveness to Appeal Romeo on Juliet (gamma2)', style=slider_style, layout=slider_layout)\n",
    "A1_slider = widgets.FloatSlider(value=2, min=0, max=10, step=0.01, description='Appeal of Romeo (A1)', style=slider_style, layout=slider_layout)\n",
    "A2_slider = widgets.FloatSlider(value=-1, min=-5, max=5, step=0.01, description='Appeal of Juliet (A2)', style=slider_style, layout=slider_layout)\n",
    "x_star2_slider = widgets.FloatSlider(value=1, min=0, max=10, step=0.01, description='x_star2', style=slider_style, layout=slider_layout)\n",
    "epsilon_slider = widgets.FloatSlider(value=0.12, min=0, max=1, step=0.01, description='Inhibition Factor Juliet (epsilon)', style=slider_style, layout=slider_layout)\n",
    "mu_slider = widgets.FloatSlider(value=100, min=0, max=1000, step=1, description='Love to Inspiration Factor Romeo (mu)', style=slider_style, layout=slider_layout)\n",
    "delta_slider = widgets.FloatSlider(value=1, min=0, max=10, step=0.01, description='Delta (delta)', style=slider_style, layout=slider_layout)\n",
    "\n",
    "sliders = [\n",
    "    alpha1_slider, alpha2_slider, beta1_slider, beta2_slider, gamma1_slider, gamma2_slider,\n",
    "    A1_slider, A2_slider, x_star2_slider, epsilon_slider, mu_slider, delta_slider\n",
    "]\n",
    "\n",
    "grid = GridBox(sliders, layout=Layout(\n",
    "    width='100%',\n",
    "    grid_template_columns='repeat(3, 32%)',  \n",
    "    grid_gap='20px 20px'\n",
    "))\n",
    "interactive_plot = interactive_output(update_plot, {\n",
    "    'alpha1': alpha1_slider, 'alpha2': alpha2_slider, 'beta1': beta1_slider, 'beta2': beta2_slider,\n",
    "    'gamma1': gamma1_slider, 'gamma2': gamma2_slider,\n",
    "    'A1': A1_slider, 'A2': A2_slider,\n",
    "    'x_star2': x_star2_slider,\n",
    "    'epsilon': epsilon_slider,\n",
    "    'mu': mu_slider,\n",
    "    'delta': delta_slider\n",
    "})\n",
    "display(grid, interactive_plot)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_plots(alpha1, alpha2, beta1, beta2, gamma1, gamma2, A1, A2, x_star2, epsilon, mu, delta):\n",
    "    params = [alpha1, alpha2, beta1, beta2, gamma1, gamma2, A1, A2, x_star2, epsilon, mu, delta]\n",
    "    solution = odeint(love_dynamics, initial_conditions, t, args=(params,))\n",
    "    \n",
    "    fig, axs = plt.subplots(1, 2, figsize=(16, 5))  # Create 1 row, 2 columns subplot\n",
    "\n",
    "    # Plot Francesco's inspiration against his love\n",
    "    axs[0].plot(solution[:, 0], solution[:, 2], label='Inspiration vs. Love', color='tab:orange')\n",
    "    axs[0].set_xlabel('Francesco\\'s Love for Laura (x1)')\n",
    "    axs[0].set_ylabel('Francesco\\'s Inspiration (z2)')\n",
    "    axs[0].set_title('Francesco\\'s Inspiration vs. His Love')\n",
    "    axs[0].legend()\n",
    "    axs[0].grid(True)\n",
    "\n",
    "    # Plot Francesco's love against Laura's love\n",
    "    axs[1].plot(solution[:, 0], solution[:, 1], label='Francesco\\'s Love vs. Laura\\'s Love', color='tab:green')\n",
    "    axs[1].set_xlabel('Francesco\\'s Love for Laura (x1)')\n",
    "    axs[1].set_ylabel('Laura\\'s Love for Francesco (x2)')\n",
    "    axs[1].set_title('Francesco\\'s Love vs. Laura\\'s Love')\n",
    "    axs[1].legend()\n",
    "    axs[1].grid(True)\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "# Parameters\n",
    "alpha1_slider = widgets.FloatSlider(value=3.6, min=-10, max=10, step=0.01, description='Forgetting Coef. Romeo (alpha1)', style=slider_style, layout=slider_layout)\n",
    "alpha2_slider = widgets.FloatSlider(value=1.2, min=0, max=10, step=0.01, description='Forgetting Coef. Juliet (alpha2)', style=slider_style, layout=slider_layout)\n",
    "beta1_slider = widgets.FloatSlider(value=1.2, min=0, max=10, step=0.01, description='Reactiveness to Love Juliet on Romeo (beta1)', style=slider_style, layout=slider_layout)\n",
    "beta2_slider = widgets.FloatSlider(value=6, min=0, max=10, step=0.01, description='Reactiveness to Love Romeo on Juliet (beta2)', style=slider_style, layout=slider_layout)\n",
    "gamma1_slider = widgets.FloatSlider(value=1.2, min=0, max=10, step=0.01, description='Reactiveness to Appeal Juliet on Romeo (gamma1)', style=slider_style, layout=slider_layout)\n",
    "gamma2_slider = widgets.FloatSlider(value=6, min=0, max=10, step=0.01, description='Reactiveness to Appeal Romeo on Juliet (gamma2)', style=slider_style, layout=slider_layout)\n",
    "A1_slider = widgets.FloatSlider(value=2, min=0, max=10, step=0.01, description='Appeal of Romeo (A1)', style=slider_style, layout=slider_layout)\n",
    "A2_slider = widgets.FloatSlider(value=-1, min=-5, max=5, step=0.01, description='Appeal of Juliet (A2)', style=slider_style, layout=slider_layout)\n",
    "x_star2_slider = widgets.FloatSlider(value=1, min=0, max=10, step=0.01, description='x_star2', style=slider_style, layout=slider_layout)\n",
    "epsilon_slider = widgets.FloatSlider(value=0.12, min=0, max=1, step=0.01, description='Inhibition Factor Juliet (epsilon)', style=slider_style, layout=slider_layout)\n",
    "mu_slider = widgets.FloatSlider(value=100, min=0, max=1000, step=1, description='Love to Inspiration Factor Romeo (mu)', style=slider_style, layout=slider_layout)\n",
    "delta_slider = widgets.FloatSlider(value=1, min=0, max=10, step=0.01, description='Delta (delta)', style=slider_style, layout=slider_layout)\n",
    "\n",
    "\n",
    "sliders = [\n",
    "    alpha1_slider, alpha2_slider, beta1_slider, beta2_slider, gamma1_slider, gamma2_slider,\n",
    "    A1_slider, A2_slider, x_star2_slider, epsilon_slider, mu_slider, delta_slider\n",
    "]\n",
    "\n",
    "# Assuming the rest of your setup (initial_conditions, t, sliders) remains unchanged\n",
    "grid = GridBox(sliders, layout=Layout(\n",
    "    width='100%',\n",
    "    grid_template_columns='repeat(3, 32%)',  \n",
    "    grid_gap='20px 20px'\n",
    "))\n",
    "interactive_plot = interactive_output(update_plots, {\n",
    "    'alpha1': alpha1_slider, 'alpha2': alpha2_slider, 'beta1': beta1_slider, 'beta2': beta2_slider,\n",
    "    'gamma1': gamma1_slider, 'gamma2': gamma2_slider,\n",
    "    'A1': A1_slider, 'A2': A2_slider,\n",
    "    'x_star2': x_star2_slider,\n",
    "    'epsilon': epsilon_slider,\n",
    "    'mu': mu_slider,\n",
    "    'delta': delta_slider\n",
    "})\n",
    "display(grid, interactive_plot)\n"
   ]
  }
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