What are Eigenvalues?

This chapter focuses on developing eigenvalues and eigenvectors (straight-line solutions) as a tool to understand the stability of an equilibrium solution. Determining eigenvalues for a linear differential equation requires computing the roots of the characteristic polynomial. The stability of the equilibrium solution is determined through the signs of the eigenvalues. This chapter shows how to compute eigenvalues and eigenvectors directly and with functions from the demodelr package. For a two-dimensional linear differential equation, all possible cases for eigenvalues, associated phase planes, and solutions are detailed.