Where can I find similar mathematic exercises like the one below? (It does not need to be related to biology, it could be about anything)
I have a book that has some mathematic models about the Lotka-Volterra equations and other kind of models but the book only gives you the model with arbitrary parameters or just gives you the model with fixed constant, i.e. it doesn't gives you the context, like in the exercise below (about bees and trees).
The name of the book is Economic Dynamics Phase Diagrams and Their Economic Application by Ronald Shone. Check page 607-608.
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.
What happens to the populations in future time?