WOB

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:

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

Figure 1
Phase-diagram of the (y₁^j, y₂^j)-values for j=0,1,...,40, $\lambda =50$ , a=0.002.