Fractalidade e crivamento na bacia de atração de estados quimera

Abstract

In this work we investigate the properties of the basin of attraction and its boundaries for chimera states in a network of nonlocally coupled Hénon maps and Roessler systems with periodic boundary conditions. It is known that coexisting basins of attraction of distinct states lead to hysteretic behaviour in diagrams in which the density of states is plotted as a function of a varying parameter. Chimera states happen when coherent and incoherent domains occur simultaneously in a network, it is believed that they emerge as a consequence of the coexistence of basins of attraction of distinct states. Consequently, the distribution of chimera states can remain invariant by a parameter modi cation, as well as may undergo sudden changes if one of the basins ceases to exist. A similar phenomenon is observed when perturbations are applied in the initial conditions. In this case the resulting e ect on the nal state of the network depends on to how the basins of attraction are organised. By means of the uncertainty exponent, we characterise the basin boundaries between the coherent and chimera states, and between the incoherent and chimera states. Estimating the volume of the basin of attraction via the basin stability calculation, we show that the density of chimera states can be not only moderately sensitive to the initial conditions, as a consequence of the existence of fractal structures in the basin, but can also be highly sensitive to initial conditions, due to the riddling in the basins of attraction