| As the discrete analogue of delay differential equations, nonlinear difference equations of higher order have numerous applications in modeling phenomena that arise in biology, ecology, physiology, physics, engineering and economics. The asymptotic behavior of the solutions of difference equations like oscillation and stability have drawn much attention in recent years. Although we are inspired by the ideas from differential equations, different techniques need to be exploited for difference equations in many cases, since the behavior of the solutions of difference equations may be quite different from the differential equations. In this dissertation, we study the global stability of the equilibrium point of three different kinds of nonlinear difference equations of higher order. All three equations arise in biological applications. |
