Topological studies of periodic orbits in the experimental Chua s circuit / Estudo topológico de órbitas periódicas no circuito experimental de Chua
AUTOR(ES)
Dariel Mazzoni Maranhão
DATA DE PUBLICAÇÃO
2006
RESUMO
We have studied the dynamical behavior of experimental time series obtained from a Chua s circuit by variation of two parameter control, $Delta R_1$ and $Delta R_2$. We investigated the chaotic and periodic behaviors of the circuit, analyzing temporal series around and inside of two periodic windows in the two-parameter space $(Delta R_1,Delta R_2)$. In the period-three window neighborhood, we analyzed how the symbolic dynamics changes when it is built by different Poincaré sections of an attractor, and we studied the dimension of return map, one- or two-dimensional, for many chaotic attractors in this region of the parameter space. In this neighborhood, we also applied topological techniques to confirm the existence of chaotic fibers: codimension one curves where the chaotic properties of the attractors remain unchanged in the two-parameter space.Around the period-four window, we investigated, by template analysis, the transition between three chaotic attractors found in the Chua s circuit. We proposed a template for chaotic regime of the circuit after merge-crisis. Finally, we investigated the bifurcations and topological structure of periodic orbits in period-three and period-four windows and also proposed a topological parameter space, based in a bimodal map model, that describe these two periodic windows.
ASSUNTO(S)
órbitas periódicas symbolic dynamics circuito de chua dinâmica simbólica caracterização topológica topological characterization molde topológico periodic orbits template chua s circuit
