**Example:** The fox squirrel is a small
mammal native to the Rocky Mountains. These squirrels are very
territorial. Note the following observations:

- if the population is large, their rate of growth decreases or even becomes negative;
- if the population is too small, fertile adults run the risk of not being able to find suitable mates, so again the rate of growth is negative

.

**1.**- Find the equilibrium (critical) points. Classify them as : source, sink or node. Justify your answers.
**2.**- Sketch the slope-field.
**3.**- Assume N=100 and M=1 and k = 1. Sketch the graph of the
solution which satisfies the initial condition
*y*(0)=20. **4.**- Assume that squirrels are emigrating (from a certain region)
with a fixed rate
*E*. Write down the new differential equation.

Also, discuss the equilibrium (critical) points under the parameter*E*. When do you observe a bifurcation?

**
**

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Contact us

Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA

users online during the last hour