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the start of my KMC practice problem - a work in progress. #7

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the start of my KMC practice problem - a work in progress. Julia
juliahmerlin Oct 7, 2025
46bddd4
Added doc string to the function
Azeezakinyemi999 Oct 7, 2025
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134 changes: 131 additions & 3 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": null,
"metadata": {},
"outputs": [],
"source": [
Expand Down Expand Up @@ -79,13 +79,141 @@
}
},
"outputs": [],
"source": [
"def monte_carlo():\n",
" \"\"\"Perform a KMC simulation of rabbits and foxes population dynamics.\"\"\"\n",
" times = []\n",
" rabbits = []\n",
" foxes = []\n",
"\n",
" time = 0\n",
" rabbit = 400\n",
" fox = 200\n",
"\n",
" times = [time] # list of times\n",
" rabbits = [rabbit] # list of rabbits\n",
" foxes = [fox] # list of foxes\n",
"\n",
" end_time = 600\n",
"\n",
" k1= 0.015\n",
" k2 = 0.00004\n",
" k3 = 0.0004\n",
" k4 = 0.04\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.cumsum()\n",
" total_rate = cumulative_rates[-1]\n",
" ut = np.random.uniform(0,1)\n",
" \n",
" if total_rate == 0:\n",
" break\n",
" \n",
" event = -1\n",
" 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",
" #carry out 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",
" time = time + ut\n",
" times.append(time)\n",
" rabbits.append(rabbit)\n",
" foxes.append(fox)\n",
" max_rabbit = max(rabbits)\n",
" rabbit_max_time_index = rabbits.index(max_rabbit)\n",
" max_rabbit_time = times[rabbit_max_time_index]\n",
"\n",
" max_fox = max(foxes)\n",
" fox_max_time_index = foxes.index(max_fox)\n",
" max_fox_time = times[fox_max_time_index]\n",
"\n",
" #plt.plot(times, rabbits , label=\"Rabbits\")\n",
" #plt.plot(times, foxes , label=\"Foxes\")\n",
" #plt.xlabel(\"Time (days)\")\n",
" #plt.ylabel(\"Population\")\n",
" #plt.xlim(0,600)\n",
" #plt.legend()\n",
" #plt.show()\n",
"\n",
" return [max_rabbit, max_rabbit_time, max_fox, max_fox_time]\n"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[401, 1.2889238279960686, 891, 600.6679963468558]\n"
]
}
],
"source": [
"values = monte_carlo()\n",
"print(values)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"#code to determine how many times we should run the code for enough precision\n",
"\n",
"num_runs = 100\n",
"max_fox_list = []\n",
"max_rabbit_list = []\n",
"time_max_fox_list = []\n",
"time_max_rabbit_list = []\n",
"\n",
"for run in range(num_runs):\n",
" values = monte_carlo()\n",
" max_rabbit = values[0]\n",
" max_rabbit_time = values[1]\n",
" max_fox = values[2]\n",
" max_fox_time = [3]\n",
" max_rabbit_list.append(max_rabbit)\n",
" time_max_rabbit_list.append(max_rabbit_time)\n",
" max_fox_list.append(max_fox)\n",
" time_max_fox_list.append(max_fox_time)\n",
"\n",
" "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "5137",
"display_name": "comp_mod_class",
"language": "python",
"name": "python3"
},
Expand All @@ -99,7 +227,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.5"
"version": "3.13.7"
}
},
"nbformat": 4,
Expand Down