Dynamics of a general model of nonlinear difference equations and its applications to LPA model

In this study, we investigate the qualitative properties of solutions to a general model of difference equations (DEs), which includes the flour beetle model as a particular case. We investigate local and global stability and boundedness, as well as the periodic behavior of the solutions to this model. Moreover, we present some general theorems that help study the periodicity of solutions to the DEs. The presented numerical examples support the finding and illustrate the behavior of the solutions for the studied model. A significant agricultural pest that is extremely resistant to insecticides is the flour beetle. Therefore, studying the qualitative characteristics of the solutions in this model greatly helps in understanding the behavior of this pest and how to resist it or benefit from it. By applying the general results to the flour beetle model, we clarify the conditions of global stability, boundedness, and periodicity.