Análise Topológica, de Observabilidade e de Sincronismo em Osciladores Caóticos: Três Estudos de Caso

Abstract

Chaotic systems present specific properties such as sensitivity to initial conditions and complex dynamics. Building such systems is relevant because they can be used in several applications such as cryptography, secure communication systems, modeling of biological systems and control of nonlinear dynamics. In this work three new chaotic systems are presented which were obtained by brute force searching. In the sequence such systems were studied in terms of topology, observability and synchronization. These systems have visual aspects that resemble the classic attractors of R\"ossler, Lorenz and Chua. However the analysis presented in this paper shows that the dynamics of the first two is different from the classical counterparts. As for the third system, more investigation is needed to establish any potential similarity.