264 lines
140 KiB
Plaintext
264 lines
140 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt\n",
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"import numpy as np"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# 8.2.3\n",
|
|
"\n",
|
|
"dt = .005\n",
|
|
"h = 3\n",
|
|
"epsilon = .01\n",
|
|
"\n",
|
|
"t = np.linspace(0,20,int(20 / dt))\n",
|
|
"A = np.zeros_like(t)\n",
|
|
"B = np.zeros_like(t)\n",
|
|
"C = np.zeros_like(t)\n",
|
|
"\n",
|
|
"A[0] = 1\n",
|
|
"for i in range (0, int(20 / dt) - 1):\n",
|
|
" A[i+1] = A[i] + dt * (epsilon + 1/(1+ (5*C[i])**h) - A[i])\n",
|
|
" B[i+1] = B[i] + dt * (epsilon + 1/(1 + (5*A[i])**h) - B[i])\n",
|
|
" C[i+1] = C[i] + dt * (epsilon + 1/(1 + (5*B[i])**h) - C[i])\n",
|
|
"\n",
|
|
"plt.title(\"Rock Paper Scissor Oscillation\")\n",
|
|
"plt.plot(t, A, label=\"A\")\n",
|
|
"plt.plot(t, B, label=\"B\")\n",
|
|
"plt.plot(t, C, label=\"C\")\n",
|
|
"plt.legend()\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 7,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# 8.2.6\n",
|
|
"\n",
|
|
"tau = 1 # can give positive interference!\n",
|
|
"dt = .05\n",
|
|
"\n",
|
|
"t = np.linspace(0,20,int(20 / dt))\n",
|
|
"x = np.zeros_like(t)\n",
|
|
"\n",
|
|
"offset = int(tau / dt)\n",
|
|
"\n",
|
|
"for i in range (0, offset):\n",
|
|
" x[i] = 1\n",
|
|
"\n",
|
|
"for i in range (offset, int(20 / dt)):\n",
|
|
" x[i] = x[i-1] - dt * (x[i-offset])\n",
|
|
"\n",
|
|
"plt.title(\"Feedback with time delay\")\n",
|
|
"plt.plot(t, x, label=\"x\")\n",
|
|
"plt.legend()\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 8,
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"sigma=1.0: found steady state after 32 iterations\n",
|
|
"E=0.0008160259005519703, T=0.0008160259005519703, s=0.0003664319324821372\n",
|
|
"sigma=2.0: found steady state after 0 iterations\n",
|
|
"E=0.000825264980790624, T=0.000825264980790624, s=0.000898694121382238\n",
|
|
"sigma=4.0: found steady state after 0 iterations\n",
|
|
"E=0.0008341652124493052, T=0.0008341652124493052, s=0.0018085373673978136\n",
|
|
"sigma=8.0: found steady state after 0 iterations\n",
|
|
"E=0.0008431183386114386, T=0.0008431183386114386, s=0.0036383427481339204\n",
|
|
"sigma=16.0: found steady state after 1 iterations\n",
|
|
"E=0.0008636293267295821, T=0.0008636293267295821, s=0.007323625346980424\n",
|
|
"sigma=32.0: found steady state after 77 iterations\n",
|
|
"E=0.0013020147363979543, T=0.0013020147363979543, s=0.018017347245352085\n",
|
|
"sigma=64.0: found steady state after 117 iterations\n",
|
|
"E=0.0033454690108945984, T=0.0033454690108945984, s=0.04922756580256679\n",
|
|
"sigma=128.0: found steady state after 94 iterations\n",
|
|
"E=0.014637594938958297, T=0.014637594938958297, s=0.1198080342996902\n",
|
|
"sigma=256.0: failed after 99999 iterations with\n",
|
|
"E=0.48076128531418244, T=0.48076128531418244, s=0\n",
|
|
"sigma=512.0: failed after 99999 iterations with\n",
|
|
"E=0.497995855519903, T=0.497995855519903, s=0\n",
|
|
"sigma=1024.0: failed after 99999 iterations with\n",
|
|
"E=0.504135476436683, T=0.504135476436683, s=0\n",
|
|
"sigma=2048.0: failed after 99999 iterations with\n",
|
|
"E=0.4813457484199005, T=0.4813457484199005, s=51.87861540862928\n",
|
|
"sigma=4096.0: failed after 99999 iterations with\n",
|
|
"E=0.48239510709524136, T=0.48239510709524136, s=103.98345045590045\n",
|
|
"sigma=8192.0: failed after 99999 iterations with\n",
|
|
"E=0.48288654803214515, T=0.48288654803214515, s=208.17878955154384\n",
|
|
"sigma=16384.0: failed after 99999 iterations with\n",
|
|
"E=0.4831239913608507, T=0.4831239913608507, s=416.5623302345357\n",
|
|
"sigma=32768.0: failed after 99999 iterations with\n",
|
|
"E=0.4832406474709451, T=0.4832406474709451, s=833.3258492804173\n",
|
|
"sigma=65536.0: failed after 99999 iterations with\n",
|
|
"E=0.48329845958357714, T=0.48329845958357714, s=1666.8511077510166\n",
|
|
"sigma=131072.0: failed after 99999 iterations with\n",
|
|
"E=0.48332723670880345, T=0.48332723670880345, s=3333.900735257699\n",
|
|
"sigma=262144.0: failed after 99999 iterations with\n",
|
|
"E=0.4833415930453797, T=0.4833415930453797, s=6667.999545646739\n",
|
|
"sigma=524288.0: failed after 99999 iterations with\n",
|
|
"E=0.4833487631579967, T=0.4833487631579967, s=13336.196944135778\n",
|
|
"sigma=1048576.0: failed after 99999 iterations with\n",
|
|
"E=0.483352346200491, T=0.483352346200491, s=26672.591629975057\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# 8.4.1\n",
|
|
"\n",
|
|
"R = 1\n",
|
|
"gamma = 1000\n",
|
|
"epsilon = .001\n",
|
|
"K = 10\n",
|
|
"KE = .1\n",
|
|
"KT = .1\n",
|
|
"\n",
|
|
"sigmas = 2 ** np.linspace(0,20,21)\n",
|
|
"Ts = np.zeros_like(sigmas)\n",
|
|
"Es = np.zeros_like(sigmas)\n",
|
|
"ss = np.zeros_like(sigmas)\n",
|
|
"\n",
|
|
"for n in range(0,21):\n",
|
|
" sigma = sigmas[n]\n",
|
|
" \n",
|
|
" if n == 0:\n",
|
|
" E = 0\n",
|
|
" T = 0\n",
|
|
" else:\n",
|
|
" E = Es[n-1]\n",
|
|
" T = Ts[n-1]\n",
|
|
" \n",
|
|
" s = sigma * T / (gamma * E + 1)\n",
|
|
"\n",
|
|
"\n",
|
|
" for i in range (int(1e5)):\n",
|
|
" Rs = R * (s / K) / (1 + (s / K))\n",
|
|
" \n",
|
|
" Enew = E + dt * (epsilon + Rs**2 / (Rs**2 + KE**2) - E)\n",
|
|
" Tnew = T + dt * (epsilon + Rs**2 / (Rs**2 + KT**2) - T)\n",
|
|
" snew = s + dt * (sigma * T - gamma * E * s - s)\n",
|
|
" \n",
|
|
" if snew < 0:\n",
|
|
" snew = 0\n",
|
|
" \n",
|
|
" if np.abs(Enew - E) < 1e-5 and np.abs(Tnew - T) < 1e-5 and np.abs(snew - s) < 1e-5:\n",
|
|
" print(f\"sigma={sigma}: found steady state after {i} iterations\")\n",
|
|
" print(f\"E={Enew}, T={Tnew}, s={snew}\")\n",
|
|
" Es[n] = Enew\n",
|
|
" Ts[n] = Tnew\n",
|
|
" ss[n] = snew\n",
|
|
" break\n",
|
|
" else:\n",
|
|
" E = Enew\n",
|
|
" T = Tnew\n",
|
|
" s = snew\n",
|
|
" \n",
|
|
" if (i == int(1e5) -1):\n",
|
|
" print(f\"sigma={sigma}: failed after {i} iterations with\")\n",
|
|
" print(f\"E={Enew}, T={Tnew}, s={snew}\")\n",
|
|
" Es[n] = Enew\n",
|
|
" Ts[n] = Tnew\n",
|
|
" ss[n] = snew\n",
|
|
" \n",
|
|
" \n",
|
|
"plt.title(\"Consumer motif\")\n",
|
|
"plt.xlabel(\"$\\sigma$\")\n",
|
|
"plt.xscale(\"log\")\n",
|
|
"plt.yscale(\"log\")\n",
|
|
"plt.plot(sigmas, Es, label=\"E\")\n",
|
|
"plt.plot(sigmas, Ts, label=\"T\")\n",
|
|
"plt.plot(sigmas, ss, label=\"s\")\n",
|
|
"plt.legend()\n",
|
|
"plt.show()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.8.10"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 4
|
|
}
|