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@lkluft
Created May 23, 2017 06:19
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Solution and visualisation of the Lotka–Volterra equations, also known as the predator–prey equations.
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{
"cells": [
{
"metadata": {
"trusted": false
},
"cell_type": "code",
"source": "%matplotlib inline\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n\ndef lotka_volterra(N, r1=2, r2=2, k1=2, k2=1):\n N1, N2 = N\n dN1 = (r1 - k1 * N2) * N1\n dN2 = (-r2 + k2 * N1) * N2\n \n return np.array([dN1, dN2])\n\n\ndef solve(initial, func=lotka_volterra, itermax=100, dt=0.1, **kwargs):\n x = np.zeros((itermax, len(initial)))\n x[0, :] = initial\n \n for i in range(itermax - 1):\n x[i+1, :] = x[i, :] + dt * func(x[i, :], **kwargs)\n \n time = np.cumsum(np.ones(itermax) * dt)\n \n return time, x\n\n\ntime, solution = solve(initial=(3, 2), itermax=10000, dt=0.001)\n\nplt.style.use('seaborn-poster')\n\nfig, ax = plt.subplots(figsize=(10, 6))\nax.plot(time, solution)\nax.legend(['Prey', 'Predator'], loc='upper left')\nax.set_xlabel('Time')\nax.set_xlim(left=0, right=np.max(time))\nax.set_ylabel('Population')\nax.set_ylim(bottom=0)\nax.set_title('Lotka-Volterra')\nfig.savefig('lotka-volterra.pdf')",
"execution_count": 1,
"outputs": [
{
"data": {
"image/png": 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QFhQUUF5ezsqVK3t9T1lZGWAET8ePHz/p9eDnVq1aRVNTEytXrqS4uNj3fHv7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HOxV56kJoti/nsu5H9nq2ktQnWJjNAdXi+PE9vDjXNCfgGjer8qmk7JQSlguWeh8VxUAkx8AMbc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\ncRBohw/e3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"text/plain": "<matplotlib.figure.Figure at 0x7ff9f1e42710>"
},
"metadata": {},
"output_type": "display_data"
}
]
}
],
"metadata": {
"kernelspec": {
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"display_name": "Python 3",
"language": "python"
},
"language_info": {
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"version": "3.6.1",
"mimetype": "text/x-python",
"codemirror_mode": {
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},
"pygments_lexer": "ipython3",
"nbconvert_exporter": "python",
"file_extension": ".py"
},
"toc": {
"toc_threshold": 6,
"toc_number_sections": true,
"toc_cell": false,
"toc_window_display": false
},
"gist": {
"id": "",
"data": {
"description": "Solution and visualisation of the Lotka–Volterra equations, also known as the predator–prey equations.",
"public": true
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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