Schedule

Abstract: In this talk, I will discuss the complex dynamics of two-dimensional discrete-time predator-prey models, focusing on a modified Leslie–Gower model with prey harvesting, and extending to three-dimensional predator-prey interactions with selective harvesting and predator self-limitation. I will also discuss the existence and stability of equilibria and utilize the bifurcation theory to examine period-doubling and Neimark-Sacker bifurcations at positive steady states. Additionally, I will demonstrate how chaos can be controlled using the Ott–Grebogi–Yorke (OGY) and hybrid control methods, providing insights into practical applications of these models. Furthermore, we are going to state open problems that will be the object of study of my PhD project.

Recently, very interesting families of branched covering maps in the plane have been studied which motivated finding similar one-dimensional maps and studying them. If we consider a branched covering map of the plane that has only one branching point and degree $2$, a good choice is to study degree $2$ circle maps. In this talk I will present all the results obtained so far for the investigation of the family of \emph{double standard maps}

\begin{equation}\label{DSM}

f_{a,b}(x)=2x+a+\frac{b}{\pi}\sin(2\pi x)\text{\ \ \ (mod 1)}.

\end{equation}

from topological results to ergodic theory.