{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"## Chaos \n",
"\n",
"#### We have learned Two Stable System Behaviors \n",
"\n",
"1. Converge to Equilibrium\n",
"2. Stable Limit Cycle\n",
"\n",
"#### Is there any other type? \n",
"\n",
"Chaos System$\\begin{cases}\n",
"\\text{Bounded Output}\\\\\n",
"\\text{Not Periodic}\n",
"\\end{cases}$"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"## Romeo Juliet System (Continuous Time Example)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"$ R' = R + 0.1J$\n",
"\n",
"$ J' = -J-T$ \n",
"\n",
"$ T' = 0.1-cT+RT$\n",
"\n",
"Let $c = 14,R(0)=5, J(0)=5, T(0)=1$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"_=var('J,R,T')\n",
"c = 14\n",
"jprime = R+0.1*J\n",
"rprime = -J-T\n",
"tprime = 0.1-c*T+R*T\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"time = srange(0,100,0.1)\n",
"sol = desolve_odeint([jprime,rprime,tprime],dvars = [J,R,T],times = time,ics = [5,5,1])"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"Graphics object consisting of 1 graphics primitive"
]
},
"execution_count": 85,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"list_plot(zip(time,sol[:,0]),plotjoined=True,axes_labels=['time','J'])"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"Graphics object consisting of 1 graphics primitive"
]
},
"execution_count": 86,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"list_plot(zip(time,sol[:,1]),plotjoined=True,axes_labels=['time','R'])"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"Graphics object consisting of 1 graphics primitive"
]
},
"execution_count": 87,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"list_plot(zip(time,sol[:,2]),plotjoined=True,axes_labels=['time','T'])"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"### It do not converge to any equilibrium point, nor stable limit cycle\n",
"\n",
"### However, it is still bounded!"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": "\n