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Question

Determine the system of differential equations corresponding to each compartment model and analyze the stability of the equilibrium (0, 0). a = 0.2, b = 0.1, c = 0, d = 0

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Since the parameters are corresponding to the parameters in the mentioned figure, we can use the matrix AA , simulating the mentioned figure with I=0I=0, by replacing the parameters by the corresponding values to simulate our system, as follows

dx(t)dt=[(0.2+0)a+c0.1b0.2a(0.1+0)b+d]x(t)=[0.20.10.20.1]x(t)\begin{align*} \dfrac{d\mathbf{x}(t)}{dt}=&\begin{bmatrix}-\overbrace{(0.2+0)}^{a+c}&\overbrace{0.1}^{b}\\\overbrace{0.2}^{a}&-\overbrace{(0.1+0)}^{b+d}\end{bmatrix}\mathbf{x}(t)\\ =&\begin{bmatrix}-0.2&0.1\\0.2&-0.1\end{bmatrix}\mathbf{x}(t) \end{align*}

Since c=0c=0 and d=0d=0, no matter leaves the system.

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