Question

3.1. Find the equilibrium points for the following dynamical systems and analyze their stability (a) $\dot{x} = x^2 - 2$ (b) $\dot{x} = x^3 - 2x^2 - x + 2$ 3.2. Find the Eigen values of the A matrix and classify the stability of the origin $\begin{pmatrix} \dot{x}_1(t) \\ \dot{x}_2(t) \end{pmatrix} = \begin{pmatrix} 2 & 1 \\ 0 & 4 \end{pmatrix} \begin{pmatrix} x_1(t) \\ x_2(t) \end{pmatrix}$ a) $\begin{pmatrix} \dot{x}_1(t) \\ \dot{x}_2(t) \end{pmatrix} = \begin{pmatrix} -1 & 3 \\ 0 & 4 \end{pmatrix} \begin{pmatrix} x_1(t) \\ x_2(t) \end{pmatrix}$ b) $\begin{pmatrix} \dot{x}_1(t) \\ \dot{x}_2(t) \end{pmatrix} = \begin{pmatrix} 2 & -1 \\ 2 & 0 \end{pmatrix} \begin{pmatrix} x_1(t) \\ x_2(t) \end{pmatrix}$ c) $\begin{pmatrix} \dot{x}_1(t) \\ \dot{x}_2(t) \end{pmatrix} = \begin{pmatrix} 0 & -1 \\ 2 & -2 \end{pmatrix} \begin{pmatrix} x_1(t) \\ x_2(t) \end{pmatrix}$ d) (2) (2) (16)

          3.1. Find the equilibrium points for the following dynamical systems and analyze their stability
(a) $\dot{x} = x^2 - 2$
(b) $\dot{x} = x^3 - 2x^2 - x + 2$
3.2. Find the Eigen values of the A matrix and classify the stability of the origin
$\begin{pmatrix} \dot{x}_1(t) \\ \dot{x}_2(t) \end{pmatrix} = \begin{pmatrix} 2 & 1 \\ 0 & 4 \end{pmatrix} \begin{pmatrix} x_1(t) \\ x_2(t) \end{pmatrix}$
a) 
$\begin{pmatrix} \dot{x}_1(t) \\ \dot{x}_2(t) \end{pmatrix} = \begin{pmatrix} -1 & 3 \\ 0 & 4 \end{pmatrix} \begin{pmatrix} x_1(t) \\ x_2(t) \end{pmatrix}$
b) 
$\begin{pmatrix} \dot{x}_1(t) \\ \dot{x}_2(t) \end{pmatrix} = \begin{pmatrix} 2 & -1 \\ 2 & 0 \end{pmatrix} \begin{pmatrix} x_1(t) \\ x_2(t) \end{pmatrix}$
c) 
$\begin{pmatrix} \dot{x}_1(t) \\ \dot{x}_2(t) \end{pmatrix} = \begin{pmatrix} 0 & -1 \\ 2 & -2 \end{pmatrix} \begin{pmatrix} x_1(t) \\ x_2(t) \end{pmatrix}$
d) 
(2)
(2)
(16)

3.1. Find the equilibrium points for the following dynamical systems and analyze their stability
(a) ẋ = x^2 - 2
(b) ẋ = x^3 - 2x^2 - x + 2
3.2. Find the Eigen values of the A matrix and classify the stability of the origin
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a)
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b)
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c)
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d)
(2)
(2)
(16)

Added by Christina M.

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