Features of basin of attractions in dynamical systems

Abstract

Evolving processes are known as dynamic systems and their behavior can be characterized through the ordered collection of data at discrete times whose rule is called discrete mapping. Although continuous information about the dynamics progress is lost in the discretization process, it is possible to identify the accessible states of the system from the knowledge of its initial configuration. Considering the scenario in which energy losses are observed due to dissipations in the dynamics, it is possible, in sufficiently long evolution times, to observe the convergence of the dynamics in the configuration space to the attractive sets of the system, generically called attractors. The set of initial conditions that converge to one of these attractors in the system is called the basins of attraction for that attractor.In systems that present multistability, the basins of attraction provide very important dynamic information about the investigated models. Depending on which basin the initial conditions are found, the system can converge to a static state or develop chaotic or periodic oscillations, contexts of important impact in real dynamic systems. This project's main objective is to study the different types of basin of attractions in discrete dynamic systems, focusing on the characterization of structural aspects such as the level of complexity associated with the boundary of the basin and its relations with the dynamic nature of the system.