**Example:** Consider the following predator-prey system

The
solution curves in the phase plane is as follows:

**1**- Sketch the
*R*(*t*)- and*F*(*t*)-graphs for the solutions with initial points*A*,*B*, and*C*. **2**- Find the longterm behavior of the populations over time.

**Answer:** First, notice that the point *A* is an equilibrium point
with non-zero coordinates. If we set

we get the following three points: (0,0), (2.5,0), and (1/0.8,1/1.5). Clearly, we have

**1**- The sketches of the
*R*(*t*)- and*F*(*t*)- graphs for the solutions with initial points*A*,*B*, and*C*respectively, are given below

**2**- It is clear that all the solutions on the phase-plane tend
to the equilibrium point A when
*t*goes to infinity. Therefore, in all the cases, we have,

and

**
**

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