Refer to a situation in which models similar to the predator-prey population models arise. Suppose A and B represent two substances that can combine to form a new substance C (chemists would write A + B → C). Suppose we have a container with a solution containing low concentrations of substances A and B, and A and B molecules react only when they happen to come close to each other. If a(t) and b(t) represent the amount of A and B in the solution, respectively, then the chance that a molecule of A is close to a molecule of B at time t is proportional to the product a(t) · b(t). Hence the rate of reaction of A and B to form C is proportional to ab. Suppose C precipitates out of the solution as soon as it is formed, and the solution is always kept well mixed.
Suppose A and B are being added to the solutions at constant (perhaps unequal) rates, and, in addition to the A + B → C reaction, a reaction B + B → A can also occur when two molecules of B are close. How would you modify your system of equations to include these assumptions?
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