Basic

We will define a simple model of water creation from hydrogen and oxygen.

First, we need to import EmptyCompartment and Species, a Synthesis reaction, and a Simulator to integrate the equations.

import numpy as np

from simbio.components import EmptyCompartment, Species
from simbio.reactions.single import Synthesis
from simbio.simulator import Simulator

To define the model, we create 3 species, corresponding to hydrogen \(H₂\), oxygen \(O₂\), and water \(H₂O\), with initial conditions of 1, 1 and 0, respectively. And we add a create_water reaction, corresponding to \(2 H₂ + O₂ → 2 H₂ O\), with a rate of 1.

class Model(EmptyCompartment):
    H2: Species = 1
    O2: Species = 1
    H2O: Species = 0

    create_water = Synthesis(A=2 * H2, B=O2, AB=2 * H2O, rate=1)

To simulate it, we feed the model named Model into Simulator, and use the .run() method. It will compile and integrate an ODE-based simulation, returning a pandas.DataFrame with the result:

simulator = Simulator(Model)

t = np.linspace(0, 10, 100)
df = simulator.run(t)
df.head()

	H2	O2	H2O
time
0.00000	1.000000	1.000000	0.000000
0.10101	0.838051	0.919025	0.161949
0.20202	0.728306	0.864153	0.271694
0.30303	0.647931	0.823965	0.352069
0.40404	0.585968	0.792984	0.414032

To visualize the time evolution, we can use the DataFrame.plot method:

df.plot()

<AxesSubplot: xlabel='time'>