CoCalc -- 2021-11-02-160604.ipynb

⁶¹⁴ views
ubuntu2004

Kernel: Python 3 (system-wide)

In [1]:

import numpy as np
import matplotlib.pyplot as plt

r_X = 1
n_hours = 8
initial_population = 1000
pop_X = np.zeros(n_hours + 1)

pop_X[0] = initial_population
for i in range(n_hours):
    pop_X[i + 1] = pop_X[i] + pop_X[i] * r_X
    
print("Population of species X:", pop_X)

Out[1]:

Population of species X: [  1000.   2000.   4000.   8000.  16000.  32000.  64000. 128000. 256000.]

In [2]:

plt.figure(figsize=(6,3))
plt.plot(pop_X)

plt.xlabel("time (hours)")
plt.ylabel("population")
plt.title("Species X")

Out[2]:

Text(0.5, 1.0, 'Species X')

In [3]:

r_Y = 0.1
n_hours = 8
initial_population = 1000
pop_Y = np.zeros(n_hours + 1)

pop_Y[0] = initial_population
for i in range(n_hours):
    pop_Y[i + 1] = pop_Y[i] + pop_Y[i] * r_Y
    
print("Population of species Y:", pop_Y)

Out[3]:

Population of species Y: [1000.      1100.      1210.      1331.      1464.1     1610.51
 1771.561   1948.7171  2143.58881]

In [4]:

plt.figure(figsize=(6,3))
plt.plot(pop_Y)

plt.xlabel("time (hours)")
plt.ylabel("population")
plt.title("Species Y")

Out[4]:

Text(0.5, 1.0, 'Species Y')

In [5]:

data_X = np.array([  1.  ,   2.18,   4.45,   8.91,  16.1 ,  31.49,  60.89, 117.58, 214.4 ]) * 1000

plt.figure(figsize=(6,3))
plt.plot(pop_X, label="model")
plt.plot(data_X, label="experiment")

plt.xlabel("time (hours)")
plt.ylabel("population")
plt.title("Species X")
plt.legend()

Out[5]:

<matplotlib.legend.Legend at 0x7fd6a84e8b80>

In [6]:

data_X = np.array([  1.  ,   2.18,   4.45,   8.91,  16.1 ,  31.49,  60.89, 117.58, 214.4 ]) * 1000

plt.figure(figsize=(6,3))
plt.plot(pop_Y, label="model")
plt.plot(data_X, label="experiment")

plt.xlabel("time (hours)")
plt.ylabel("population")
plt.title("Species Y")
plt.legend()

Out[6]:

<matplotlib.legend.Legend at 0x7fd6a8546b80>

In [7]:

data_X = np.loadtxt("data_exp_X.txt")
print(data_X)

r_X = 1
n_hours = 24
initial_population = 1000
pop_X = np.zeros(n_hours + 1)

pop_X[0] = initial_population
for i in range(n_hours):
    pop_X[i + 1] = pop_X[i] + pop_X[i] * r_X
    
plt.figure(figsize=(6,3))
plt.plot(pop_X, label="model")
plt.plot(data_X, label="experiment")

plt.xlabel("time (hours)")
plt.ylabel("population")
plt.title("Species X")
plt.legend()

Out[7]:

[1.00000000e+03 2.17777342e+03 4.44576258e+03 8.91456547e+03
60958432e+04 3.14897238e+04 6.08883077e+04 1.17580768e+05
14397399e+05 3.81989811e+05 6.03315856e+05 7.87285829e+05
96982461e+05 1.04405640e+06 1.08337178e+06 9.95533440e+05
79746583e+05 9.72332987e+05 9.21969859e+05 1.04273060e+06
43221236e+05 9.37714865e+05 9.85877957e+05 1.07409317e+06]

<matplotlib.legend.Legend at 0x7fd6a844f6a0>

In [8]:

plt.figure(figsize=(6,3))
plt.plot(data_X, color='#ff7f0e')

Out[8]:

[<matplotlib.lines.Line2D at 0x7fd6a81ef1f0>]

In [9]:

data_X = np.loadtxt("data_exp_X.txt")
print(data_X)

r_X = 1
K_X = 1e6
n_hours = 24
initial_population = 1000
pop_X = np.zeros(n_hours + 1)

pop_X[0] = initial_population
for i in range(n_hours):
    pop_X[i + 1] = pop_X[i] + (1 - pop_X[i]/K_X) * r_X * pop_X[i]
    
plt.figure(figsize=(6,3))
plt.plot(pop_X, label="model")
plt.plot(data_X, label="experiment")

plt.xlabel("time (hours)")
plt.ylabel("population")
plt.title("Species X")
plt.legend()

Out[9]:

[1.00000000e+03 2.17777342e+03 4.44576258e+03 8.91456547e+03
60958432e+04 3.14897238e+04 6.08883077e+04 1.17580768e+05
14397399e+05 3.81989811e+05 6.03315856e+05 7.87285829e+05
96982461e+05 1.04405640e+06 1.08337178e+06 9.95533440e+05
79746583e+05 9.72332987e+05 9.21969859e+05 1.04273060e+06
43221236e+05 9.37714865e+05 9.85877957e+05 1.07409317e+06]

<matplotlib.legend.Legend at 0x7fd6a81ab700>

In [10]:

data_Y = np.loadtxt("data_exp_Y.txt")
print(data_Y)

r_Y = 0.4
K_Y = 1e5
n_hours = 24
initial_population = 1000
pop_Y = np.zeros(n_hours + 1)

pop_Y[0] = initial_population
for i in range(n_hours):
    pop_Y[i + 1] = pop_Y[i] + (1 - pop_Y[i]/K_Y) * r_Y * pop_Y[i]
    
plt.figure(figsize=(6,3))
plt.plot(pop_Y, label="model")
plt.plot(data_Y, label="experiment")

plt.xlabel("time (hours)")
plt.ylabel("population")
plt.title("Species Y")
plt.legend()

Out[10]:

[ 1000.          1468.8176607   2017.57949899  2807.82253178
57884669  5880.69829402  7977.64738035 10987.23896838
68925539 22778.96386341 27118.703459   32395.04050862
5970265  37400.13541081 40923.61000019 43399.85608048
14014915 51923.92262397 48936.98814589 53081.08029097
24903328 49175.42023105 50032.49399002 50577.54776097]

<matplotlib.legend.Legend at 0x7fd6a806fa90>

In [11]:

data_A = np.loadtxt("data_exp_A.txt")
print(data_A)

r_A = 0.9
K_A = 1e6
n_hours = 24
initial_population = 1000
pop_A = np.zeros(n_hours + 1)

pop_A[0] = initial_population
for i in range(n_hours):
    pop_A[i + 1] = pop_A[i] + (1 - pop_A[i]/K_A) * r_A * pop_A[i]
    
plt.figure(figsize=(6,3))
plt.plot(pop_A, label="model")
plt.plot(data_A, label="experiment")

plt.xlabel("time (hours)")
plt.ylabel("population")
plt.title("Species A")
plt.legend()

print("data from experiment A fits the model when r (the growth rate) = 0.9")

Out[11]:

[  1000.           1815.38733857   3448.85956215   5798.61439409
  10814.57619309  21383.8241311   41567.08370915  80314.28400864
 149785.58154461 265585.75112717 365411.1780143  491689.65445915
 481846.55931036 512615.59044084 484702.74364789 557117.06357226
 577315.88799858 536066.67437239 587459.10894856 522740.85774677
 541827.5414437  544308.07661042 511645.32546393 547557.6806335 ]
data from experiment A fits the model when r (the growth rate) = 0.9

In [12]:

data_B = np.loadtxt("data_exp_B.txt")
print(data_B)

r_B = 0.4
K_B = .5e5
n_hours = 24
initial_population = 10000
pop_B = np.zeros(n_hours + 1)

pop_B[0] = initial_population
for i in range(n_hours):
    pop_B[i + 1] = pop_B[i] + (1 - pop_B[i]/K_B) * r_B * pop_B[i]
    
plt.figure(figsize=(6,3))
plt.plot(pop_B, label="model")
plt.plot(data_B, label="experiment")

plt.xlabel("time (hours)")
plt.ylabel("population")
plt.title("Species B")
plt.legend()

print("data from experiment B fits the model when r (the growth rate) = 0.4")

Out[12]:

[10000.         14459.72616873 19131.64692025 24238.72992793
68997643 31945.75133898 36640.34691545 41360.91604431
35660568 47444.96450721 48857.57934742 47687.15960361
80325624 55773.3720636  60200.29157554 58068.40452503
84038794 53861.60465174 50108.26898469 54439.73015449
25171659 49774.81127443 51135.06372078 56478.91948071]
data from experiment B fits the model when r (the growth rate) = 0.4

In [13]:

data_C = np.loadtxt("data_exp_C.txt")
print(data_C)

r_C = 0.7
K_C = 1e5
n_hours = 24
initial_population = 1000
pop_C = np.zeros(n_hours + 1)

pop_C[0] = initial_population
for i in range(n_hours):
    pop_C[i + 1] = pop_C[i] + (1 - pop_C[i]/K_C) * r_C * pop_C[i]
    
plt.figure(figsize=(6,3))
plt.plot(pop_C, label="model")
plt.plot(data_C, label="experiment")

plt.xlabel("time (hours)")
plt.ylabel("population")
plt.title("Species C")
plt.legend()

print("data from experiment C fits the model when r (the growth rate) = 0.7")

Out[13]:

[  1000.           1713.24432864   2744.49898211   4449.95419272
   7662.63408538  12526.09381011  19450.42606159  30143.888785
  46748.25020832  71004.59399994  81066.7935574   90233.10312421
  94121.25320283  87729.32306957  92361.26302922  93968.98534754
 105341.48590974 102981.44000993  94634.96172829 103248.79824022
 101238.10227826  93521.06457228  96575.99191112  97826.04612173]
data from experiment C fits the model when r (the growth rate) = 0.7

In [0]:

In [0]:

In [0]:

In [0]:

In [0]:

Product

Resources

Company