{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# [Chapter 4](https://github.com/Ziaeemehr/spikes/blob/main/examples/chap_04.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### **Higher dimensional linear systems**\n",
"\n",
"Code by : Abolfazl Ziaeemehr \n",
"- https://github.com/Ziaeemehr\n",
"\n",
"
"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# uncomment and run this line to install the package on colab\n",
"# !pip install \"git+https://github.com/Ziaeemehr/spikes.git\" -q"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import sympy\n",
"import sympy as sp\n",
"import numpy as np\n",
"from scipy.linalg import eig\n",
"from IPython.display import display, Math\n",
"\n",
"sympy.init_printing()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Eq. 4.2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\n",
"\\frac{d}{dt}\n",
"\\begin{pmatrix}\n",
"E_1 \\\\\n",
"E_2 \\\\\n",
"E_3\n",
"\\end{pmatrix} =\n",
"\\begin{pmatrix}\n",
"-5 & -10 & 7 \\\\\n",
" 7& -5& -10 \\\\\n",
" -10& 7 & -5 \n",
"\\end{pmatrix} \n",
"\\begin{pmatrix}\n",
"E_1 \\\\\n",
"E_2 \\\\\n",
"E_3\n",
"\\end{pmatrix}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"A = np.array([[-5, -10, 7], [7, -5, -10], [-10, 7, -5]])\n",
"B = np.array([0,0,0])\n",
"X0 = np.array([1, -5, 7])\n",
"t_range = np.linspace(0, 2, 1000)\n",
"\n",
"# eigenvalues, eigenvectors = eig(A)\n",
"# eigenvalues"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle x_1(t) = e^{- 8 t} + 4 \\sqrt{3} e^{- \\frac{7 t}{2}} \\sin{\\left(\\frac{17 \\sqrt{3} t}{2} \\right)}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle x_2(t) = e^{- 8 t} - 2 \\sqrt{3} e^{- \\frac{7 t}{2}} \\sin{\\left(\\frac{17 \\sqrt{3} t}{2} \\right)} - 6 e^{- \\frac{7 t}{2}} \\cos{\\left(\\frac{17 \\sqrt{3} t}{2} \\right)}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle x_3(t) = e^{- 8 t} - 2 \\sqrt{3} e^{- \\frac{7 t}{2}} \\sin{\\left(\\frac{17 \\sqrt{3} t}{2} \\right)} + 6 e^{- \\frac{7 t}{2}} \\cos{\\left(\\frac{17 \\sqrt{3} t}{2} \\right)}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from spikes.solver import solve_system_of_equations\n",
"\n",
"final_solution, x_values = solve_system_of_equations(A, B, X0, t_range)\n",
"\n",
"for i, sol in enumerate(final_solution, 1):\n",
" display(Math(f'x_{i}(t) = {sp.latex(sol)}'))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- plot the evaluation of analytical solution over a given time interval:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from sympy import lambdify\n",
"import matplotlib.pyplot as plt\n",
"\n",
"plt.figure(figsize=(6, 4))\n",
"for i in range(3):\n",
" plt.plot(t_range, x_values[i], label=f\"x{i+1}(t)\")\n",
"\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Value')\n",
"plt.margins(x=0.01)\n",
"plt.title('Solutions of the System of Differential Equations')\n",
"plt.legend();\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Numerical solution to compare:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.integrate import odeint\n",
"\n",
"def system(X, t, A):\n",
" return A.dot(X)\n",
"\n",
"A = np.array([[-5, -10, 7],\n",
" [7, -5, -10],\n",
" [-10, 7, -5]])\n",
"X0 = np.array([1, -5, 7])\n",
"\n",
"# Time points\n",
"t = np.linspace(0, 2, 1000)\n",
"solution_numerical = odeint(system, X0, t, args=(A,))\n",
"\n",
"plt.figure(figsize=(6, 4))\n",
"for i in range(3):\n",
" plt.plot(t_range, x_values[i], label=f\"x{i+1}(t)\", alpha=0.5)\n",
" plt.plot(t, solution_numerical[:, i], 'k--', label=f\"x{i+1} num\", alpha=0.5)\n",
" \n",
"\n",
"plt.xlabel('Time')\n",
"plt.ylabel('Value')\n",
"plt.margins(x=0.01)\n",
"plt.title('Solutions of the System of Differential Equations')\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 4.3 Oscillatory control of respiration"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\operatorname{Poly}{\\left( x^{2} + 3 x + 2, x, domain=\\mathbb{Z} \\right)}$"
],
"text/plain": [
"Poly(x**2 + 3*x + 2, x, domain='ZZ')"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import sympy\n",
"from spikes.utils import routh\n",
"from spikes.utils import characteristic_polynomial\n",
"# Example usage\n",
"matrix = [[0, 1], [-2, -3]]\n",
"polynomial = characteristic_polynomial(matrix)\n",
"HR = routh(polynomial)\n",
"polynomial"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}1 & 2\\\\3 & 0\\\\2 & 0\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[1, 2],\n",
"[3, 0],\n",
"[2, 0]])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"HR"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"⎡-3 0 -g -5⎤\n",
"⎢ ⎥\n",
"⎢-5 -3 0 -g⎥\n",
"⎢ ⎥\n",
"⎢-g -5 -3 0 ⎥\n",
"⎢ ⎥\n",
"⎣0 -g -5 -3⎦\n"
]
}
],
"source": [
"g = sympy.Symbol('g')\n",
"A = sympy.Matrix([\n",
" [-3, 0, -g, -5],\n",
" [-5, -3, 0, -g],\n",
" [-g, -5, -3, 0],\n",
" [0, -g, -5, -3]\n",
"])\n",
"p = characteristic_polynomial(A)\n",
"sympy.pprint(A)"
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {},
"outputs": [],
"source": [
"# p"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [],
"source": [
"# HR = routh(p)\n",
"# HR"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For stability, the left hand column must have entries with all the same signs"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [],
"source": [
"# sympy.solve([e > 0 for e in HR[:, 0]], g)"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{2 - g: 1, -g - 8: 1, g - 3 - 5*I: 1, g - 3 + 5*I: 1}"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A.eigenvals()# , A.eigenvects()"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[2 - g, -g - 8, g - 3 - 5*I, g - 3 + 5*I]"
]
},
"execution_count": 62,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"char_poly = A.charpoly().as_expr()\n",
"lam = sympy.Symbol('lambda')\n",
"eigenvalues = sp.solve(char_poly, lam)\n",
"eigenvalues"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"so to have oscillatory behaviour, we need to have a pair of complex conjugates eigenvalues, with real part of zero or negative and imaginary part of non-zero.\n",
"\n",
"```python\n",
"g - 3 + 5 * I\n",
"g - 3 - 5 * I\n",
"\n",
"g = 3\n",
"```"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"language_info": {
"name": "python"
}
},
"nbformat": 4,
"nbformat_minor": 4
}