Caos e sincronização em circuitos eletrônicos com realimentação atrasada. - Oliveira Junior, Gilson Francisco de (2012)
In this work we studied the dynamics of electronic circuits described by nonlinear equations. We first reproduced some results from the literature for chaos generation in low-frequency circuits and we obtained synchronism between two coupled systems each circuit being a time-delay first-order circuit. In a second step, we built an original system of second-order LRC oscillator, with delayed feedback. We characterized the signal of this system for several parameters through usual signal analysis techniques. We were able to identify a variety of states of this oscillator, evolving from periodic to chaotic states. Using numerical simulations we reproduced every observed scenario. We studied how two equivalent chaotic oscillators behave when unidirectional coupling is applied, i.e. when the second oscillator has its dynamics controlled by a signal from the first oscillator. Using the correlation function we showed that the systems are synchronized. We also studied transient phenomena in the error signal of two coupled time-delay second-order circuits. Analyzing the difference between the dynamical variables of these circuits we can observe escapes of synchronization which occur when the error signal, for brief moments, goes far away from its mean value. We try to characterize the amplitude and frequency of these synchronization escapes as a function of a coupling parameter or adding of noise to the coupling signal.