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2024-08-31 12:07:21 +03:00

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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"vscode": {
"languageId": "python"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[-2.952193285082998?, 0.8954506854014756?, 3.528371299840761? - 2.389151018830233?*I, 3.528371299840761? + 2.389151018830233?*I]"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A=matrix([[1,7,3,3],[-2,5,1,1],[1,2,-2,1],[1,-1,3,1]])\n",
"A.eigenvalues()"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"vscode": {
"languageId": "python"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"log(u(t)) == t + log(u(t) - 1) - 80143857/25510582*I - 28672937/13049616\n",
"limit(log(u(t)), t, +Infinity) == limit(t + log(u(t) - 1) - 80143857/25510582*I - 28672937/13049616, t, +Infinity)\n"
]
}
],
"source": [
"t = var('t')\n",
"u = function('u')(t)\n",
"de = diff(u,t) == u*(1-u)\n",
"sol = desolve(de, u, ics=[0,0.1])\n",
"sol = solve(sol,u)[0]\n",
"print(sol)\n",
"l=limit(sol,t=oo)\n",
"print(l)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"vscode": {
"languageId": "python"
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"Graphics object consisting of 3 graphics primitives"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x, y = var('x y')\n",
"\n",
"\n",
"f =(x*(1-x-(1/2)*y), y*(1-y))\n",
"p=plot_vector_field(f,(x,-5,5),(y,-5,5))\n",
"sol = desolve_odeint((f[0],f[1]), [1/4,1/2], srange(0, 10000, 0.1), [x,y])\n",
"sol2 = desolve_odeint(f, [1,1/2], srange(0, 10000, 0.1), [x,y])\n",
"p+=line(zip(sol[:,0], sol[:,1]))\n",
"p+=line(zip(sol2[:,0], sol2[:,1]), color='red')\n",
"\n",
"show(p)"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"vscode": {
"languageId": "python"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[x == 0, y == 0]\n",
"[1, 1]\n",
"[x == 1, y == 0]\n",
"[-1, 1]\n",
"[x == 0, y == 1]\n",
"[1/2, -1]\n",
"[x == (1/2), y == 1]\n",
"[-1/2, -1]\n"
]
}
],
"source": [
"\n",
"x, y = var('x y')\n",
"\n",
"\n",
"f =(x*(1-x-(1/2)*y), y*(1-y))\n",
"\n",
"j = jacobian(f, (x,y))\n",
"\n",
"\n",
"#solve for f=(0,0)\n",
"sol = solve([f[0]==0,f[1]==0],x,y)\n",
"\n",
"\n",
"# find eigenvalues for jacobian of all points\n",
"for i in sol:\n",
" print(i)\n",
" j2 = j.subs(x=i[0].rhs(),y=i[1].rhs())\n",
" print(j2.eigenvalues())\n",
"\n",
"\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 9.5",
"language": "sage",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "sage",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.6"
},
"orig_nbformat": 4
},
"nbformat": 4,
"nbformat_minor": 2
}