# Example Of Analyzing a Nonlinear Biochemical System


```python
import sympy
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sympy import init_session
init_session()
```

    IPython console for SymPy 1.7 (Python 3.6.9-64-bit) (ground types: python)
    
    These commands were executed:
    >>> from __future__ import division
    >>> from sympy import *
    >>> x, y, z, t = symbols('x y z t')
    >>> k, m, n = symbols('k m n', integer=True)
    >>> f, g, h = symbols('f g h', cls=Function)
    >>> init_printing()
    
    Documentation can be found at https://docs.sympy.org/1.7/
    



```python
Integral(sqrt(1/x),x)
```


```python
da, A, a, x, k1, k2, db, b, B, k3, k4 = symbols('da A a x k1 k2 db b B k3 k4')
da = -(A - a)*x*k1+ k2*a
db = -k3*(B-b)*a - b*k4*(A-a)
solve([da, db], [a, b])
```


```python

```


```python
from sympy import solve

xdd, z, dxx, xZ, x, g, zdd, ydd, yZ, y, Ldy, zZ, zdd, Ldz = symbols("xdd z dxx xZ x g zdd ydd yZ y Ldy zZ zdd Ldz")

E1 = z * xdd + (xZ - x) * (g + zdd)
E2 = z * ydd + (yZ - y) * (g + zdd) - Ldy
E3 = -y * xdd + x * ydd - zZ * (g + zdd) + Ldz

sols = solve([E1, E2, E3], [xdd, ydd, Ldy])

print ("xdd = ", (sols[xdd]).factor())
print ("ydd = ", (sols[ydd]).factor())
print ("Ldy = ", (sols[Ldy]).factor())
```

    xdd =  (g + zdd)*(x - xZ)/z
    ydd =  (-Ldz*z + g*x*y - g*xZ*y + g*z*zZ + x*y*zdd - xZ*y*zdd + z*zZ*zdd)/(x*z)
    Ldy =  (-Ldz*z + g*x*yZ - g*xZ*y + g*z*zZ + x*yZ*zdd - xZ*y*zdd + z*zZ*zdd)/x


c980b632eec1cf2255b2db527a33657fd53c6de0
ipynb
Jupyter Notebook
Example of Nonlinear Analysis.ipynb
joseph-hellerstein/NonlinearAnalysis
e1aeb7b7a7431b6a15c9ad3dde676ccf5aff0807
MIT
Example of Nonlinear Analysis.ipynb
joseph-hellerstein/NonlinearAnalysis
e1aeb7b7a7431b6a15c9ad3dde676ccf5aff0807
MIT
Example of Nonlinear Analysis.ipynb
joseph-hellerstein/NonlinearAnalysis
e1aeb7b7a7431b6a15c9ad3dde676ccf5aff0807
MIT
Qwen/Qwen-72B
1. YES
2. YES