ABSTRACT
Earlier we briefly considered systems of equations when converting an nth-order equation to a system of n first-order equations. But systems of differential equations arise in their own right—whenever there is more than one dependent variable for an independent variable. For example, one might consider a system with two or more interacting species with the population sizes changing over time. The most common of these are known as Lotka– Volterra models and are discussed in detail in Section 6.5. One of these models is a predator–prey system in which the prey population growth depends upon the number of predators that kill the prey. Similarly, the rate at which the predator population grows depends on the size of their food supply, namely, the prey population. In general, these conditions produce nonlinear equations that are very difficult to solve analytically. This is just one scenario we can consider. In this chapter, we discuss methods for solving these types of systems.
