##Ejercicio 4 Practica 1
Para cada uno de los siguientes sistemas encontrar todos los puntos de equilibrio y determinar el tipo de cada punto de equilibio aislado.
 * b) 
 
 $$\left\{ \begin{array}{lcc}
            \dot{x}_{1}=-x_{1}+x_{2}\\
             \\ \dot{x}_{2}=\frac{x_{1}}{10}-2x_{1}-x_{1}^{2}-\frac{x_{1}^{3}}{10}
             \end{array}
\right.$$


```python
import sympy as sym
```


```python
#Con esto las salidas van a ser en LaTeX
sym.init_printing(use_latex=True)
```


```python
x_1, x_2 = sym.symbols('x_1 x_2')
```


```python
X = sym.Matrix([x_1, x_2])
X
```


```python
f_1 = -x_1 + x_2
```


```python
f_2 = sym.Rational(1,10) * x_1 - 2 * x_2 - x_1 ** 2 - sym.Rational(1,10) * x_1 ** 3
```


```python
F = sym.Matrix([f_1,f_2])
```


```python
F
```


```python
A = F.jacobian(X)
A
```


```python
# puntos de equilibrio del sistema
pes = sym.solve([f_1,f_2])
pes
```


```python
type(pes[0])
```




    dict




```python
A_1 = A.subs(pes[0])
A_1
```


```python
A_1.eigenvals() 
```


```python
A_2 = A.subs(pes[1])
A_2
```


```python
lambda_2 = A_2.eigenvals()
lambda_2
```


```python
sym.N(lambda_2.keys()[0])
```


```python
sym.N(lambda_2.keys()[1])
```


```python
A_3 = A.subs(pes[2])
A_3
```


```python
lambda_3 = A_3.eigenvals()
lambda_3
```


```python
sym.N(lambda_3.keys()[0])
```


```python
sym.N(lambda_3.keys()[1])
```


```python

```

026afe9a00cae5938e6af90f25cbca0cd7be3a7e
ipynb
Jupyter Notebook
Practica1_eje4_b.ipynb
elsuizo/Nonlinear_systems
9636d4a450339b8c735934923810c9539ac76042
MIT
Practica1_eje4_b.ipynb
elsuizo/Nonlinear_systems
9636d4a450339b8c735934923810c9539ac76042
MIT
Practica1_eje4_b.ipynb
elsuizo/Nonlinear_systems
9636d4a450339b8c735934923810c9539ac76042
MIT
Qwen/Qwen-72B
1. YES
2. YES