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Richard - Added in-class edits, and an answer notebook. #13

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1f28061
Edits made in class. Incomplete
rwest Oct 7, 2025
587cc87
Added an answer notebook
rwest Oct 7, 2025
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324 changes: 324 additions & 0 deletions rabbits-and-foxes-kmc-answer.ipynb
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92 changes: 91 additions & 1 deletion rabbits-and-foxes-kmc-question.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -23,7 +23,7 @@
},
{
"cell_type": "code",
"execution_count": 1,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
Expand Down Expand Up @@ -62,13 +62,27 @@
"Make sure you've done enough simulations to be suitably confident in your answers (given the precision you think appropriate)."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Your turn!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Done in class, on Friday October 3rd, 2025"
]
},
{
"cell_type": "code",
"execution_count": null,
Expand All @@ -79,6 +93,82 @@
}
},
"outputs": [],
"source": [
"\n",
"time = 0\n",
"rabbit = 400\n",
"fox = 200\n",
"\n",
"times = [time]\n",
"rabbits = [rabbit]\n",
"foxes = [fox]\n",
"\n",
"end_time = 600\n",
"\n",
"k1 = 0.015 # Rabbit birth rate /day\n",
"k2 = 0.00004 # Rabbit death /day/fox\n",
"k3 = 0.0004 # Fox birth rate /day/rabbit\n",
"k4 = 0.04 # Fox death rate /day\n",
"\n",
"while time < end_time:\n",
" rate_rabbit_birth = k1 * rabbit\n",
" rate_rabbit_death = k2 * rabbit * fox\n",
" rate_fox_birth = k3 * rabbit * fox\n",
" rate_fox_death = k4 * fox\n",
"\n",
" rates = np.array([rate_rabbit_birth, rate_rabbit_death,\n",
" rate_fox_birth, rate_fox_death])\n",
" cumulative_rates = rates.cumsum()\n",
" total_rate = cumulative_rates[-1]\n",
"\n",
" u = np.random.uniform(0, 1)\n",
" event = -1 # invalid event\n",
" for i, cum_rate in enumerate(cumulative_rates):\n",
" if cum_rate / total_rate > u:\n",
" event = i\n",
" break\n",
" # carry out the event\n",
" if event == 0:\n",
" rabbit += 1\n",
" elif event == 1:\n",
" rabbit -= 1\n",
" elif event == 2:\n",
" fox += 1\n",
" elif event == 3:\n",
" fox -= 1\n",
" else:\n",
" raise ValueError(\"event not in 0,1,2,3\")\n",
"\n",
" break # exit the loop, while it's incomplete"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"for n in range(10):\n",
" u = np.random.uniform(0, 1)\n",
" for i, cum_rate in enumerate(cumulative_rates):\n",
" if cum_rate / total_rate > u:\n",
" event = i\n",
" break\n",
" print(u, event)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
Expand Down