Let $B$ be number of bees per acre, measured in hundreds of bees, while $C$ is the weight of trees per acre, in thousands of pounds. Suppose that the time is measured in months. $$\frac{dB}{dt}=.1(1-.01B+.005C)B$$ $$\frac{dC}{dt}=.03(1+.04B-.1C)C$$ Suppose one acre of land has 10,000 pounds of trees in it, and a beehive of 2,000 bees is introduced...(1)
What happens to the populations in future time?
What I've done:
I found all the equilibrium points and I analyze each of them.
$1. (0,0), 2.(0,1/.1), 3.(1/.01,0), 4.(525/4,125/2)$
- and 4. are source points and the rest of them are saddle points.
I also draw the phase portrait, but I don't know how to relate the information given in (1).
As you can see none of the equilibrium points are stable so I can't use this $lim_{t\to\infty}B(t)=\overline x$.
Can someone help me to answer the question please?
I greatly appreciate any assistance you may provide.
Around the nontrivial fixed point: