Model of student migration

exm1
Variables and parameters:

y1(t): number of students studying option 1

y2(t): number of students studying option 2

$\lambda$: input of fresh students per time interval $\Delta t$

a: effectiveness of communication between the students y1 and y2

$\beta$: backflow from y2 to y1 ( $\beta =0.1$)

d1: rate of successful final examination of y1 (d1=0.1)

d2: rate of successful final examination of y2 (d2=0.3)

$\gamma$: portion of graduate students ( $\gamma=0.4$)


mapping:

\begin{displaymath}y_1(t_{j+1}) &=y_1(t_j)+\lambda-a(t_j)y_1(t_j)y_2(t_j)+\beta y_2(t_j)-d_1y_1(t_j)\cr \end{displaymath}


\begin{displaymath}y_2(t_{j+1}) &=y_2(t_j)+a(t_j)y_1(t_j)y_2(t_j)-\beta y_2(t_j)-d_2y_2(t_j)\cr\end{displaymath}

bounds:

\begin{displaymath}y_1\geq 0,\quad y_2\geq 0,\quad a(t)y_1(t)y_2(t)\leq \gamma y_1(t),\quad a(t)\leq a_{\max}\end{displaymath}



Comments


Figure 1
Phase-diagram of the (y1j, y2j)-values for j=0,1,...,40, $\lambda =50$, a=0.002.

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