Abstract
This chapter explains the stability of a nonlinear delay difference equation in population dynamics. Insect and fish populations with nonoverlapping generations may be described by scalar first-order nonlinear difference equations. Recent mathematical studies by Li and York, and May suggest that this class of population models can have a wide range of dynamical behavior. Conversely, data for many insect populations, which have been assembled by Hassell, Lawton and May, suggest that most insect populations in the field have stable dynamics. The use of Liapunov functions for population models is generally limited to a system with one or two state variables. This is because it is usually impossible to verify that a function of three or more variables is negative definite.
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