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62 changes: 58 additions & 4 deletions 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": 4,
"metadata": {},
"outputs": [],
"source": [
Expand Down Expand Up @@ -79,13 +79,67 @@
}
},
"outputs": [],
"source": []
"source": [
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"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 # birth rate of rabbits /day\n",
"k2 = 0.00004 # death rate of rabbits due to foxes /day\n",
"k3 = 0.0004 # birth rate of foxes due to rabbits /day\n",
"k4 = 0.04 # death rate of foxes /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, rate_fox_birth, rate_fox_death])\n",
" cumulative_rates = rates\n",
" total_rate = cumulative_rates[-1]\n",
"\n",
" u = np.random.uniform(0,1)\n",
" break # exit loop while its incomplete\n",
" "
]
},
{
"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 )\n",
" "
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "5137",
"display_name": "jb",
"language": "python",
"name": "python3"
},
Expand All @@ -99,7 +153,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.5"
"version": "3.12.11"
}
},
"nbformat": 4,
Expand Down