Linear Discrete Dynamical Systems

Aims and Objectives

• To introduce recurrence relations for first- and second-order difference equations.

• To introduce the theory of the Leslie model.

• To apply the theory to modeling the population of a single species.

On completion of this chapter, the reader should be able to

• solve first- and second-order homogeneous linear difference equations;

• find eigenvalues and eigenvectors of matrices;

• model a single population with different age classes;

• predict the long-term rate of growth/decline of the population;

• investigate how harvesting and culling policies affect the model.