Estatística de falhas de sincronismo entre circuitos elétricos caóticos - Oliveira Junior, Gilson Francisco de (2016)
We study experimentally and numerically, desynchronization event statistics that occur in coupled chaotic systems. Such studies are conducted through coupled chaotic electronic circuits, operating in intermittent synchronization regime. The observed results are reproduced numerically by routines that integrates their nonlinear ordinary differential equations. At the beginning of this work, we reproduce some results of the literature to demonstrate that coupled chaotic oscillators may have intermittent synchronism when they are expected to have complete synchronism, according to criteria already established in the literature for synchronization. The reason for this fault of synchronization is the presence of unstable objects immersed in the chaotic attractor of the system, which reduce the stability of the synchronized state. We reproduce, also, the analysis of bursts from complete synchronization state which follow a nonnormal distribuition, where the events of greatest amplitude escape from the distribution of events of small and medium amplitude, and they can be predicted. In the last Chapter of this thesis we show our three results about the statistics of desynchronization events and how to controll them. These results presented here were carried out in a second-order non-autonomous system that we built in two configurations and allow us to explore different behaviors. We characterize the signals from the first system using different parameters and we use analysis techniques that could identify a variety of states of the oscillators between regular and chaotic. We reproduce all scenarios observed experimentally through numerical simulations. To study the level of synchronization between these two oscillators, almost-identical and coupled unidirectionally via negative feedback, we build a variable named error signal which measures the difference between the responses of the two oscillators. The coupling efficiency to generate full synchronism is verified and using the system under intermittent synchronism we characterize the desynchronization events measured by the so-called error signal. In this non-autonomous system we use the observed error signal following power-law type distributions, and that this power law exponent varies depending on the coupling parameter. As this non-autonomous system may display different chaotic states which differ in the visitation rate at the central region of its phase space, we characterized the desynchronization events for some of chaotic attractors and observed that the greater the entrance rate in the central region of the phase space, the greater the occurrence of the desynchronization events of large amplitude. For an investigation of the occurrence of extreme events we build a second, second-order non-autonomous system, a modified version of the first system. We characterize this second system, verifying that the unstable objects immersed in the chaotic attractor are unstable periodic orbits, unlike other results from the literature where instability is a saddle point. With this second system we have our third result, we modify the instability of the synchronized state by means of a single parameter so that the desynchronization events turns to follow a non-normal distribution composed of two contributions, one following a power-law and the other where the events are dragon-king type. Thus, we show the possibility of control for the frequency of these extreme events.