Conclusion
Bifurcation structures in discrete time nonlinear systems

Bifurcation structures associated with specific nonlinearities have been presented. We have described nested-box and queued-box bifurcation structures through generic examples and particular examples of engineering systems. Knowledge of these structures enables us to apprehend the behaviors that appear in certain nonlinear systems and to understand their evolution when parameters vary, in particular the routes to chaos. The aims of these studies are twofold: on the one hand, to understand how chaotic behavior arises in order to eliminate the parameters that induce this type of phenomenon, and on the other, to obtain chaos for use in specific applications such as secure transmissions or pseudo-random number generation.

These studies can be generalized. A high-degree polynomial transformation with several extrema will produce a BE-like structure, but the more extrema,...