{
"cells": [
{
"cell_type": "markdown",
"id": "a9f7c338-338f-4372-b6d1-77708fe1e87d",
"metadata": {},
"source": [
"1. Consider the continuous-time whale problem given by\n",
"$$\\eqalign{\n",
" {dB\\over dt}&=0.05 B\\Big(1- {B\\over 150000}\\Big)-\\alpha BF\\cr\\cr\n",
" {dF\\over dt}&=0.08 F\\Big(1- {F\\over 400000}\\Big)-\\alpha BF\\cr\n",
"}$$\n",
"We will use simulation to explore the fractal limit\n",
"sets for the discrete approximations of the continuous system\n",
"using Euler's method for different step sizes $h$.\n"
]
},
{
"cell_type": "markdown",
"id": "17ca4f7f-a566-40b9-9d40-2ccb43ea65ad",
"metadata": {},
"source": [
"(i) Let $X=(B,F)$ and write the above system as $dX/dt=G(X)$.\n",
"What is $G(X)$?"
]
},
{
"cell_type": "markdown",
"id": "e9649c7a-f962-4aa3-b119-43162a723485",
"metadata": {},
"source": [
"The above system can be written as $dX/dt=G(X)$ where\n",
"$$\n",
" X=\\left[\\matrix{B\\cr F}\\right] \\qquad\\hbox{and}\\qquad\n",
" G(X)=\\left[\\matrix{\n",
" 0.05 B(1- B/150000)-\\alpha BF\\cr\n",
" 0.08 F(1- F/400000)-\\alpha BF\n",
" }\\right].\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "3c99e7ab-86d9-4956-9afc-6a81933e0dd6",
"metadata": {},
"source": [
"(ii) Suppose the initial whale populations\n",
"are $B_0=5000$ blue whales and $F_0=70000$ fin whales.\n",
"Let $\\alpha=10^{-8}$ and use a computer implementation\n",
"of the Euler method\n",
"$$X_{n+1}=X_n+h G(X_n)\n",
"\\qquad\\hbox{with}\\qquad h=32$$\n",
"to plot the population of fin whales for the\n",
"times $t_n=hn$ where $n=0,1,\\ldots,50$.\n",
"This may be done in Julia as\n",
" \n",
"```\n",
" Xn=X0; Xs=[X0]; h=32\n",
" for n=1:50\n",
" Xn=Xn+h*G(Xn...)\n",
" push!(Xs,Xn)\n",
" end\n",
" scatter(h*(0:50),last.(Xs),\n",
" xlabel=\"years\",ylabel=\"Fin whales\",label=false)\n",
"```\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "126c6a18-eaa5-43d8-9033-777f80fdac11",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2-element Vector{Float64}:\n",
" 5000.0\n",
" 70000.0"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"G(B,F)=[0.05*B*(1-B/150000)-alpha*B*F,\n",
" 0.08*F*(1-F/400000)-alpha*B*F]\n",
"alpha=1e-8\n",
"B0=5000.0; F0=70000.0\n",
"X0=[B0,F0]"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "b670be34-43e4-47a4-91ce-aea61ff8d333",
"metadata": {},
"outputs": [],
"source": [
"using Plots"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "ed4761c7-a644-44a0-8bd5-399e346d5890",
"metadata": {},
"outputs": [
{
"data": {
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",
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\")
"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Xn=X0; Xs=[X0]; h=32\n",
"for n=1:50\n",
" Xn=Xn+h*G(Xn...)\n",
" push!(Xs,Xn)\n",
"end\n",
"scatter(h*(0:50),last.(Xs),\n",
" xlabel=\"years\",ylabel=\"Fin whales\",label=false)"
]
},
{
"cell_type": "markdown",
"id": "ab1b22a8-acc2-4f0c-91aa-82ad58856ab3",
"metadata": {},
"source": [
"(iii) Plot blue whales $B_n$ versus fin whales $F_n$ for\n",
"$n=100,101,\\ldots,1000$. This may be done in Julia as\n",
"\n",
"```\n",
" Xn=X0; Xs=[X0]; h=32\n",
" for n=1:1000\n",
" Xn=Xn+h*G(Xn...)\n",
" push!(Xs,Xn)\n",
" end\n",
" scatter(first.(Xs[101:end]),last.(Xs[101:end]),\n",
" xlabel=\"Blue whales\",ylabel=\"Fin whales\",label=false)\n",
"```\n",
"\n",
"Your graph should show the limit set consisting of four points."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "7304f4e6-1e33-4bd6-9bf5-25b433d8a86d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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